Polynomials

Problem 1

Multiply and simplify $(2x - 5)(3x - 3)$

See Solution

Problem 2

Expand the expression $(x-5)(x+2)$ .

See Solution

Problem 3

Multiply and simplify $(2x - 5)(3x - 3)$ .

See Solution

Problem 4

Multiply and simplify: $(2x - 5)(3x - 3)$

See Solution

Problem 5

Expand $(x-5)(x+2)$ using the FOIL method.

See Solution

Problem 6

Multiply and simplify: $(2x - 5)(3x - 3)$ .

See Solution

Problem 7

Multiply and simplify $(2x - 5)(3x - 3)$ .

See Solution

Problem 8

Multiply and simplify $(2x-5)(3x-3)$ .

See Solution

Problem 9

Multiply and simplify: $(2x-5)(3x-3)$ .

See Solution

Problem 10

Multiply and simplify $(2 x-5)(3 x-3)$ .

See Solution

Problem 11

Find all solutions for the function $f(x)=2 x^{3}-6 x^{2}+9 x-27$ .

See Solution

Problem 12

Simplify $(3 x^{2}-16 x+21) \div (x-3)$ .

See Solution

Problem 13

Solve the equation $x^{4}-2 x^{3}-3 x^{2}=0$ .

See Solution

Problem 14

Solve the equation $4(t-3)^{3}(t-5)^{2}+2(t-3)^{4}(t-5)=0$ .

See Solution

Problem 15

Express the polynomial $\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}$ in sigma notation. Which option is correct?

See Solution

Problem 16

Multiply and simplify $(2 x-5)(3 x-3)$ .

See Solution

Problem 17

Find the largest common factor of $3 x^{3} y + 2 x^{2} y^{2}$ . Options: a) $6 x^{3} y^{2}$ , b) $6 x^{5} y^{3}$ , c) $x^{2} y$ , d) $x^{3} y^{2}$ , e) $2 x^{2} y$ .

See Solution

Problem 18

Factor $16 x^{4}-1$ . Choose the correct option from: a) $(2 x-1)^{2}(2 x+1)^{2}$ , b) $(4 x-1)^{2}(4 x+1)^{2}$ , c) $(2 x-1)(2 x+1)(4 x^{2}+1)$ , d) $(2 x-1)(2 x+1)(2 x^{2}-1)$ , e) $(2 x-1)(2 x+1)(2 x^{2}+1)$ .

See Solution

Problem 19

Simplify the expression: $21 j^{8} k^{3} l^{3} \div 3 k^{2} l$ .

See Solution

Problem 20

Find $x$ such that $f(x)=0$ for $f(x)=x^{3}-3x+1$ using the Intermediate Value Theorem.

See Solution

Problem 21

Expand the expression $(4+3 x)^{5}$ .

See Solution

Problem 22

Solve the equation by factoring: $x^{3}+5 x^{2}-4 x-20=0$ .

See Solution

Problem 23

Divide $2 x + 7$ into $2 x ^ { 4 } + 21 x ^ { 3 } + 35 x ^ { 2 } - 37 x + 46$ .

See Solution

Problem 24

Calculate the product of $x(2x + 4)$ .

See Solution

Problem 25

Simplifica la expresión: $\frac{x^{3}-1}{x-1}-\frac{x^{3}+1}{x+1}$ .

See Solution

Problem 26

Factorice $P(x, y) = x^{2} y + z^{2} w + x^{2} w$ .

See Solution

Problem 27

Determina el grado de $P(x ; y)=x^{3 b+2} y^{6}+7 x^{6} y^{2 a+}$ respecto a "x".

See Solution

Problem 28

Si $P(x ; y)=x^{3 n+5} y^{5 n-2} z^{2}$ tiene grado 26 en $x$ , ¿cuál es el grado en $y$ ?

See Solution

Problem 29

Simplify the expression: $4(4 a-9 b)+(3 a+5 b)$ .

See Solution

Problem 30

Combine the expressions: $(4 a-9 b)+(3 a+5 b)$ . What is the simplified result?

See Solution

Problem 31

Multiply the expressions: $(u+3y)(2u-y)$ .

See Solution

Problem 32

Find the square of the expression: $(2-\sqrt{3 x-1})^2$ .

See Solution

Problem 33

Find the degree of the polynomial $8 y^{3}-9 y^{2}+8$ .

See Solution

Problem 34

Determine the degree of the polynomial $4x^{2}-7x+4$ .

See Solution

Problem 35

Arrange the polynomial $9 x^{2} + 8 - 2 x^{3}$ in ascending order of the powers of $x$ .

See Solution

Problem 36

Add the polynomials: $3p - 4q + 4r$ , $2p + 3q - 8r$ , and $q - 6p + r$ .

See Solution

Problem 37

Factor the expression: $(7 x^{5} y^{2}+5 x^{4} y^{3})(7 x^{5} y^{2}-5 x^{4} y^{3})$ .

See Solution

Problem 38

Calculate $\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)$ .

See Solution

Problem 39

Simplify the expression: $\left(5 x^{9} y^{4}-11\right)^{3}$ .

See Solution

Problem 40

Simplify $\left(9 x y^{2}+10 x^{3} y^{4}\right)^{4}$ .

See Solution

Problem 41

Simplify the expression $(8 x^{2}+9 x)^{5}$ .

See Solution

Problem 42

Simplify the expression: $(8 x^{2}+5 x)^{5}$ .

See Solution

Problem 43

Simplify $5 a^{2} + 3 b - 2 a^{2} - 5 b$ and $8 k^{3} \div 2 k + 5 x^{3} - 7 k^{2} + 2 x^{3}$ .

See Solution

Problem 44

Simplify: $\left(a^{2}+b^{2}+c^{2}\right)(a b-b c-a c)$

See Solution

Problem 45

Simplify the expression $(2 a-b+3 c)(2 a-b-3 c)$ .

See Solution

Problem 46

Find the value of the constant $c$ in $f(x)=2x^3+3x^2+cx+8$ given $f$ intersects the $x$ -axis at $(-4,0)$ , $(\frac{1}{2},0)$ , and $(p,0)$ .

See Solution

Problem 47

Find the constant $c$ in the function $f(x)=x^{3}+1.5 x^{2}+\frac{1}{2} c x+4$ given roots at $(-4,0)$ , $(\frac{1}{2}, 0)$ , and $(t, 0)$ .

See Solution

Problem 48

Find constants $h$ and $k$ such that $(x-4)(x+h)+2 \equiv(x-5)^{2}+k$ , then calculate $h+k$ .

See Solution

Problem 49

Evaluate $4 a^{3}-2 b$ for $a=2$ and $b=-3$ .

See Solution

Problem 50

Evaluate $2 x^{3}-4 y^{2}$ for $x=-2$ and $y=-3$ .

See Solution

Problem 51

Multiply (6 x² - 5 x + 3) by (3 x² + 7 x - 3) and simplify the result.

See Solution

Problem 52

Simplify: $2 x^{2}(x+2)-3 x(x^{2}-3)-5 x(x+5)$ to find the result.

See Solution

Problem 53

Simplify $2 x^{2}(x+2)-3 x(x^{2}-3)-5 x(x+5)$ .

See Solution

Problem 54

Classify the polynomials and find their degrees.
1. The polynomial $3x^{2}$ is a with a degree of .
2. The polynomial $x^{2}y + 3xy^{2} + 1$ is a with a degree of .

See Solution

Problem 55

What is the first term of Alina's polynomial in standard form after simplifying $x y^{2}-2 x^{2} y+3 y^{3}-6 x^{2} y+4 x y^{2}$ ? Options: $x y^{2}$ , $5 x y^{2}$ , $-8 x^{2} y$ , $-2 x^{2} y$ .

See Solution

Problem 56

What is the first term of Alina's polynomial in standard form if the last term is $3 y^{3}$ ? The polynomial is $x y^{2}-2 x^{2} y+3 y^{3}-6 x^{2} y+4 x y^{2}$ . Options: 1. $x y^{2}$ 2. $5 x y^{2}$ 3. $-8 x^{2} y$ 4. $-2 x^{2} y$

See Solution

Problem 57

Determine the correct statement about the polynomial $5 s^{6} t^{2}+6 s t^{9}-8 s^{6} t^{2}-6 t^{7}$ .

See Solution

Problem 58

Find the missing first term to create a degree 4 binomial from: -5xy^{3} + 9x^{2}y. Choose 3 options: 0, 5xy^{3}, 9x^{2}y, 8y^{4}, 4xy^{3}.

See Solution

Problem 59

Identify the polynomial among these expressions: $4 x^{2}-3 x+\frac{2}{x}$ , $-6 x^{3}+x^{2}-\sqrt{5}$ , $8 x^{2}+\sqrt{x}$ , $-2 x^{4}+\frac{3}{2 x}$ .

See Solution

Problem 60

Identify the trinomial among these expressions: $x^{3}+x^{2}-\sqrt{x}$ , $2 x^{3}-x^{2}$ , $4 x^{3}+x^{2}-\frac{1}{x}$ , $x^{6}-x+\sqrt{6}$ .

See Solution

Problem 61

Find the missing exponent on $m$ in the polynomial $-2 m^{2} n^{3}+2 m^{2} n^{3}+7 n^{2}-6 m^{4}$ so it becomes a degree 4 binomial. Options: 0, 1, 2, 4.

See Solution

Problem 62

What is the first term of Julian's polynomial in standard form if the last term is $-3 x^{4}$ ? Options: 1. $4 y^{4}$ 2. $6 y^{4}$ 3. $-2 x y^{3}$ 4. $-10 x y^{3}$

See Solution

Problem 63

Julian simplifies the polynomial: $4 x^{2} y^{2}-2 y^{4}-8 x y^{3}+9 x^{3} y+6 y^{4}-2 x y^{3}-3 x^{4}+x^{2} y^{2}$ . What is the first term in standard form? Options: $4 y^{4}$ , $6 y^{4}$ , $-2 x y^{3}$ , $-10 x y^{3}$ .

See Solution

Problem 64

Determine the true statement about the polynomial $3 j^{4} k-2 j k^{3}+j k^{3}-2 j^{4} k+j k^{3}$ after simplification.

See Solution

Problem 65

If $x$ is a positive integer such that $(x-1)(x-3)(x-5)\ldots(x-93)<0$ , how many values can $x$ take?

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Problem 66

Factorize: $2 a^{7}-128 a$

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Problem 67

Multiply (6x² - 5x + 3) by (3x² + 7x - 3).

See Solution

Problem 68

Prove that $(3a+2b+3c)^{3}=(a+b)^{3}+(b+2c)^{3}+(c+2a)^{3}+450$ for constants $a$ , $b$ , $c$ .

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Problem 69

Simplify the expression: $4x - 2x + 8 + 3x - 1$ .

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Problem 70

Divide the polynomial $P(x)=4x^{3}-2x^{2}-x+1$ by $g(x)=x+4$ .

See Solution

Problem 71

Calculate the sum of the following expressions:
$(3 y^{2}+y^{3}-5)+(4 y^{2}-4 y+2 y^{3}+8)$ $(3 y^{3}+7 y^{2}-4 y+3)$ $(4 y^{2}+3 y^{3}-y+3)$ $(-y^{4}+2 y^{3}-y-4)$ $(4 y^{3}+3 y^{2}-3 y+1)$

See Solution

Problem 72

Calculate the product of $(p^{2}-q^{2})(p^{4}+q^{4})$ .

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Problem 73

Multiply the binomials $(3y-8)(5y-1)$ and check the result for $x=0$ and $y=-2$ .

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Problem 74

Calculate $\frac{30+320+24+256}{15}$ and find the product $(x-2y)(3x^{2}-2xy+2y^{2})$ .

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Problem 75

Calculate the product of $(a^{2} b - 2)$ and $(5 - a b^{2})$ .

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Problem 76

Find the product: $(x-2y)(3x^{2}-2xy)2y^{2}$ .

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Problem 77

Calculate $\left(a^{2}+a b+b^{2}\right) \times(a-b)$ .

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Problem 78

Find three consecutive odd integers such that the sum of the smallest and largest equals 150. What are the integers?

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Problem 79

Find values of $a$ , $b$ , and $c$ for $f(x)=x^{3}+5$ based on given pairs: $a=f(0)$ , $b=f^{-1}(32)$ , $c=f(7)$ . Select correct option.

See Solution

Problem 80

Find $n$ if the coefficient of $x^{2}$ in $\left(\frac{1}{2}+2 x\right)(1-3 x)^{n}$ is 108.

See Solution

Problem 81

Simplify the expression: $24(2 x^{2}) + 10 \times \left(\frac{55}{x^{2}}\right) + 10\left(2 \times \left(\frac{55}{2 x^{2}}\right)\right)$ .

See Solution

Problem 82

Simplify the expression: $12(4 x^{2}) + 5\left(6 x\left(\frac{55}{2 x^{2}}\right)\right)$ .

See Solution

Problem 83

Find the coefficient of $x^{3}$ in the expansion of $(3 + 2x)^{6}$ .

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Problem 84

Convert "The sum of the least and greatest of three consecutive odd integers is 122" into a polynomial and find the first integer.

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Problem 85

Identify a function that fits the points $(-2, 8)$ , $(1, 5)$ , $(3, 13)$ , and $(5, 29)$ .

See Solution

Problem 86

Simplify: $(3 q^{2}+p q) \times \frac{p}{q^{2}(p+3 q)}.$

See Solution

Problem 87

Simplify the expression: $2 a^{2} b(-2) a b$ .

See Solution

Problem 88

Simplify the expression: $\frac{10 x^{8}}{5 x^{4}}$ .

See Solution

Problem 89

Simplify the expression: $-10(-8 x + 9) - 8 x$ .

See Solution

Problem 90

Simplify the expression: $9(7k + 8) + 3(k - 10)$ .

See Solution

Problem 91

Simplify the expression: $-10(x-7)-7(x+2)$ .

See Solution

Problem 92

Simplify the expression $12y - 4w + 4y + 6w$ .

See Solution

Problem 93

Multiply $8xy$ by $3y$ . What is the result?

See Solution

Problem 94

Calculate the product of $8xy$ and $3y$ .

See Solution

Problem 95

Simplify the expression: $9 - 6w + 5$ .

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Problem 96

Identify the trinomial from the options: A. $\sqrt{3 x}+1$ , B. $\frac{7+x}{2}$ , C. $x+3$ , D. $3 x^{2}+4 x+1$ .

See Solution

Problem 97

Find the coefficient in $8 x^{2}+1$ . A. 2 B. 8 C. 1 D. $x$

See Solution

Problem 98

Which option shows the polynomial $2 x^{2}-4 x+x^{6}+8+3 x^{10}$ in descending order?

See Solution

Problem 99

Factor the expression: $6a - 48$

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Problem 100

Factor the following expressions:
1. $45, 70, 85$
2. $35, 49, 77$
3. $x^{5} y^{3}, x^{6} y^{6}$
4. $x^{7} y^{2} z, x^{9} y^{4} z^{2}$
5. $98 x^{5} y^{3}, 110 x^{4} y^{4}, 26 x^{2} y^{5}$
6. $18 x^{7} y^{3} z, 42 x^{3} y^{4} z, 72 x^{4} y z^{2}$
7. $-15 x y z, -55 x y^{2}, -55 y z$
8. $9 x^{3} y^{7}, -18 x y^{2}, -36 y^{3}$
9. $32 x^{5} y^{3}, 48 x^{4} y^{3}, -48 x^{5} y^{4}$
10. $24 x^{4} y^{3}, 84 x^{4} y^{3}, 168 x^{5} q^{4}$
11. $6 a - 48$
12. $21 b + 63 b^{2}$
13. $12 c - 28 d + 52$
14. $-4 e^{2} + 7 e^{3} - 9 e^{4}$
15. $14 f^{3} + 42 f^{5} - 77 f^{7}$
16. $24 g^{2} - 39 g h + 51 h^{2}$
17. $42 j^{2} k - 78 j k^{3} + 66 j^{3} k^{4}$
18. $18 m^{4} n^{4} - 63 m^{5} n^{3} + 117 m^{6} n^{2}$
19. $-8 p^{3} q - 16 p^{2} - p^{8} q$
20. $36 r s^{2} - 72 r^{2} s + 60 r s$

See Solution

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306

Polynomials

Problem 1

Multiply and simplify (2x−5)(3x−3) (2x - 5)(3x - 3) (2x−5)(3x−3)

Problem 2

Expand the expression (x−5)(x+2)(x-5)(x+2)(x−5)(x+2).

Problem 3

Multiply and simplify (2x−5)(3x−3) (2x - 5)(3x - 3) (2x−5)(3x−3).

Problem 4

Multiply and simplify: (2x−5)(3x−3) (2x - 5)(3x - 3) (2x−5)(3x−3)

Problem 5

Expand (x−5)(x+2) (x-5)(x+2) (x−5)(x+2) using the FOIL method.

Problem 6

Multiply and simplify: (2x−5)(3x−3)(2x - 5)(3x - 3)(2x−5)(3x−3).

Problem 7

Multiply and simplify (2x−5)(3x−3) (2x - 5)(3x - 3) (2x−5)(3x−3).

Problem 8

Multiply and simplify (2x−5)(3x−3) (2x-5)(3x-3) (2x−5)(3x−3).

Problem 9

Multiply and simplify: (2x−5)(3x−3) (2x-5)(3x-3) (2x−5)(3x−3).

Problem 10

Multiply and simplify (2x−5)(3x−3)(2 x-5)(3 x-3)(2x−5)(3x−3).

Problem 11

Find all solutions for the function f(x)=2x3−6x2+9x−27f(x)=2 x^{3}-6 x^{2}+9 x-27f(x)=2x3−6x2+9x−27.

Problem 12

Simplify (3x2−16x+21)÷(x−3) (3 x^{2}-16 x+21) \div (x-3) (3x2−16x+21)÷(x−3).

Problem 13

Solve the equation x4−2x3−3x2=0x^{4}-2 x^{3}-3 x^{2}=0x4−2x3−3x2=0.

Problem 14

Solve the equation 4(t−3)3(t−5)2+2(t−3)4(t−5)=04(t-3)^{3}(t-5)^{2}+2(t-3)^{4}(t-5)=04(t−3)3(t−5)2+2(t−3)4(t−5)=0.

Problem 15

Express the polynomial 52x3+3x4+72x5+4x6\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}25​x3+3x4+27​x5+4x6 in sigma notation. Which option is correct?

Problem 16

Multiply and simplify (2x−5)(3x−3)(2 x-5)(3 x-3)(2x−5)(3x−3).

Problem 17

Find the largest common factor of 3x3y+2x2y23 x^{3} y + 2 x^{2} y^{2}3x3y+2x2y2. Options: a) 6x3y26 x^{3} y^{2}6x3y2, b) 6x5y36 x^{5} y^{3}6x5y3, c) x2yx^{2} yx2y, d) x3y2x^{3} y^{2}x3y2, e) 2x2y2 x^{2} y2x2y.

Problem 18

Problem 19

Simplify the expression: 21j8k3l3÷3k2l21 j^{8} k^{3} l^{3} \div 3 k^{2} l21j8k3l3÷3k2l.

Problem 20

Find xxx such that f(x)=0f(x)=0f(x)=0 for f(x)=x3−3x+1f(x)=x^{3}-3x+1f(x)=x3−3x+1 using the Intermediate Value Theorem.

Problem 21

Expand the expression (4+3x)5(4+3 x)^{5}(4+3x)5.

Problem 22

Solve the equation by factoring: x3+5x2−4x−20=0x^{3}+5 x^{2}-4 x-20=0x3+5x2−4x−20=0.

Problem 23

Divide 2x+72 x + 72x+7 into 2x4+21x3+35x2−37x+462 x ^ { 4 } + 21 x ^ { 3 } + 35 x ^ { 2 } - 37 x + 462x4+21x3+35x2−37x+46.

Problem 24

Calculate the product of x(2x+4)x(2x + 4)x(2x+4).

Problem 25

Simplifica la expresión: x3−1x−1−x3+1x+1 \frac{x^{3}-1}{x-1}-\frac{x^{3}+1}{x+1} x−1x3−1​−x+1x3+1​.

Problem 26

Factorice P(x,y)=x2y+z2w+x2wP(x, y) = x^{2} y + z^{2} w + x^{2} wP(x,y)=x2y+z2w+x2w.

Problem 27

Determina el grado de P(x;y)=x3b+2y6+7x6y2a+P(x ; y)=x^{3 b+2} y^{6}+7 x^{6} y^{2 a+}P(x;y)=x3b+2y6+7x6y2a+ respecto a "x".

Problem 28

Si P(x;y)=x3n+5y5n−2z2P(x ; y)=x^{3 n+5} y^{5 n-2} z^{2}P(x;y)=x3n+5y5n−2z2 tiene grado 26 en xxx, ¿cuál es el grado en yyy?

Problem 29

Simplify the expression: 4(4a−9b)+(3a+5b)4(4 a-9 b)+(3 a+5 b)4(4a−9b)+(3a+5b).

Problem 30

Combine the expressions: (4a−9b)+(3a+5b)(4 a-9 b)+(3 a+5 b)(4a−9b)+(3a+5b). What is the simplified result?

Problem 31

Multiply the expressions: (u+3y)(2u−y)(u+3y)(2u-y)(u+3y)(2u−y).

Problem 32

Find the square of the expression: (2−3x−1)2(2-\sqrt{3 x-1})^2(2−3x−1​)2.

Problem 33

Find the degree of the polynomial 8y3−9y2+88 y^{3}-9 y^{2}+88y3−9y2+8.

Problem 34

Determine the degree of the polynomial 4x2−7x+44x^{2}-7x+44x2−7x+4.

Problem 35

Arrange the polynomial 9x2+8−2x39 x^{2} + 8 - 2 x^{3}9x2+8−2x3 in ascending order of the powers of xxx.

Problem 36

Add the polynomials: 3p−4q+4r3p - 4q + 4r3p−4q+4r, 2p+3q−8r2p + 3q - 8r2p+3q−8r, and q−6p+rq - 6p + rq−6p+r.

Problem 37

Factor the expression: (7x5y2+5x4y3)(7x5y2−5x4y3)(7 x^{5} y^{2}+5 x^{4} y^{3})(7 x^{5} y^{2}-5 x^{4} y^{3})(7x5y2+5x4y3)(7x5y2−5x4y3).

Problem 38

Calculate (7x5y2+5x4y3)(7x5y2−5x4y3)\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)(7x5y2+5x4y3)(7x5y2−5x4y3).

Problem 39

Simplify the expression: (5x9y4−11)3\left(5 x^{9} y^{4}-11\right)^{3}(5x9y4−11)3.

Problem 40

Simplify (9xy2+10x3y4)4\left(9 x y^{2}+10 x^{3} y^{4}\right)^{4}(9xy2+10x3y4)4.

Multiply and simplify $(2x - 5)(3x - 3)$

Expand the expression $(x-5)(x+2)$ .

Multiply and simplify $(2x - 5)(3x - 3)$ .

Multiply and simplify: $(2x - 5)(3x - 3)$

Expand $(x-5)(x+2)$ using the FOIL method.

Multiply and simplify: $(2x - 5)(3x - 3)$ .

Multiply and simplify $(2x - 5)(3x - 3)$ .

Multiply and simplify $(2x-5)(3x-3)$ .

Multiply and simplify: $(2x-5)(3x-3)$ .

Multiply and simplify $(2 x-5)(3 x-3)$ .

Find all solutions for the function $f(x)=2 x^{3}-6 x^{2}+9 x-27$ .

Simplify $(3 x^{2}-16 x+21) \div (x-3)$ .

Solve the equation $x^{4}-2 x^{3}-3 x^{2}=0$ .

Solve the equation $4(t-3)^{3}(t-5)^{2}+2(t-3)^{4}(t-5)=0$ .

Express the polynomial $\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}$ in sigma notation. Which option is correct?

Multiply and simplify $(2 x-5)(3 x-3)$ .

Find the largest common factor of $3 x^{3} y + 2 x^{2} y^{2}$ . Options: a) $6 x^{3} y^{2}$ , b) $6 x^{5} y^{3}$ , c) $x^{2} y$ , d) $x^{3} y^{2}$ , e) $2 x^{2} y$ .

Simplify the expression: $21 j^{8} k^{3} l^{3} \div 3 k^{2} l$ .

Find $x$ such that $f(x)=0$ for $f(x)=x^{3}-3x+1$ using the Intermediate Value Theorem.

Expand the expression $(4+3 x)^{5}$ .

Solve the equation by factoring: $x^{3}+5 x^{2}-4 x-20=0$ .

Divide $2 x + 7$ into $2 x ^ { 4 } + 21 x ^ { 3 } + 35 x ^ { 2 } - 37 x + 46$ .

Calculate the product of $x(2x + 4)$ .

Simplifica la expresión: $\frac{x^{3}-1}{x-1}-\frac{x^{3}+1}{x+1}$ .

Factorice $P(x, y) = x^{2} y + z^{2} w + x^{2} w$ .

Determina el grado de $P(x ; y)=x^{3 b+2} y^{6}+7 x^{6} y^{2 a+}$ respecto a "x".

Si $P(x ; y)=x^{3 n+5} y^{5 n-2} z^{2}$ tiene grado 26 en $x$ , ¿cuál es el grado en $y$ ?

Simplify the expression: $4(4 a-9 b)+(3 a+5 b)$ .

Combine the expressions: $(4 a-9 b)+(3 a+5 b)$ . What is the simplified result?

Multiply the expressions: $(u+3y)(2u-y)$ .

Find the square of the expression: $(2-\sqrt{3 x-1})^2$ .

Find the degree of the polynomial $8 y^{3}-9 y^{2}+8$ .

Determine the degree of the polynomial $4x^{2}-7x+4$ .

Arrange the polynomial $9 x^{2} + 8 - 2 x^{3}$ in ascending order of the powers of $x$ .

Add the polynomials: $3p - 4q + 4r$ , $2p + 3q - 8r$ , and $q - 6p + r$ .

Factor the expression: $(7 x^{5} y^{2}+5 x^{4} y^{3})(7 x^{5} y^{2}-5 x^{4} y^{3})$ .

Calculate $\left(7 x^{5} y^{2}+5 x^{4} y^{3}\right)\left(7 x^{5} y^{2}-5 x^{4} y^{3}\right)$ .

Simplify the expression: $\left(5 x^{9} y^{4}-11\right)^{3}$ .

Simplify $\left(9 x y^{2}+10 x^{3} y^{4}\right)^{4}$ .

Simplify the expression $(8 x^{2}+9 x)^{5}$ .

Simplify the expression: $(8 x^{2}+5 x)^{5}$ .

Simplify $5 a^{2} + 3 b - 2 a^{2} - 5 b$ and $8 k^{3} \div 2 k + 5 x^{3} - 7 k^{2} + 2 x^{3}$ .

Simplify: $\left(a^{2}+b^{2}+c^{2}\right)(a b-b c-a c)$

Simplify the expression $(2 a-b+3 c)(2 a-b-3 c)$ .

Find the value of the constant $c$ in $f(x)=2x^3+3x^2+cx+8$ given $f$ intersects the $x$ -axis at $(-4,0)$ , $(\frac{1}{2},0)$ , and $(p,0)$ .

Find the constant $c$ in the function $f(x)=x^{3}+1.5 x^{2}+\frac{1}{2} c x+4$ given roots at $(-4,0)$ , $(\frac{1}{2}, 0)$ , and $(t, 0)$ .

Find constants $h$ and $k$ such that $(x-4)(x+h)+2 \equiv(x-5)^{2}+k$ , then calculate $h+k$ .

Evaluate $4 a^{3}-2 b$ for $a=2$ and $b=-3$ .

Evaluate $2 x^{3}-4 y^{2}$ for $x=-2$ and $y=-3$ .

Simplify: $2 x^{2}(x+2)-3 x(x^{2}-3)-5 x(x+5)$ to find the result.

Simplify $2 x^{2}(x+2)-3 x(x^{2}-3)-5 x(x+5)$ .

Classify the polynomials and find their degrees.
1. The polynomial $3x^{2}$ is a with a degree of .
2. The polynomial $x^{2}y + 3xy^{2} + 1$ is a with a degree of .

What is the first term of Alina's polynomial in standard form after simplifying $x y^{2}-2 x^{2} y+3 y^{3}-6 x^{2} y+4 x y^{2}$ ? Options: $x y^{2}$ , $5 x y^{2}$ , $-8 x^{2} y$ , $-2 x^{2} y$ .

Determine the correct statement about the polynomial $5 s^{6} t^{2}+6 s t^{9}-8 s^{6} t^{2}-6 t^{7}$ .

Identify the polynomial among these expressions: $4 x^{2}-3 x+\frac{2}{x}$ , $-6 x^{3}+x^{2}-\sqrt{5}$ , $8 x^{2}+\sqrt{x}$ , $-2 x^{4}+\frac{3}{2 x}$ .

Identify the trinomial among these expressions: $x^{3}+x^{2}-\sqrt{x}$ , $2 x^{3}-x^{2}$ , $4 x^{3}+x^{2}-\frac{1}{x}$ , $x^{6}-x+\sqrt{6}$ .

Find the missing exponent on $m$ in the polynomial $-2 m^{2} n^{3}+2 m^{2} n^{3}+7 n^{2}-6 m^{4}$ so it becomes a degree 4 binomial. Options: 0, 1, 2, 4.

What is the first term of Julian's polynomial in standard form if the last term is $-3 x^{4}$ ? Options: 1. $4 y^{4}$ 2. $6 y^{4}$ 3. $-2 x y^{3}$ 4. $-10 x y^{3}$

Determine the true statement about the polynomial $3 j^{4} k-2 j k^{3}+j k^{3}-2 j^{4} k+j k^{3}$ after simplification.

If $x$ is a positive integer such that $(x-1)(x-3)(x-5)\ldots(x-93)<0$ , how many values can $x$ take?

Factorize: $2 a^{7}-128 a$

Prove that $(3a+2b+3c)^{3}=(a+b)^{3}+(b+2c)^{3}+(c+2a)^{3}+450$ for constants $a$ , $b$ , $c$ .

Simplify the expression: $4x - 2x + 8 + 3x - 1$ .

Divide the polynomial $P(x)=4x^{3}-2x^{2}-x+1$ by $g(x)=x+4$ .

Calculate the product of $(p^{2}-q^{2})(p^{4}+q^{4})$ .

Multiply the binomials $(3y-8)(5y-1)$ and check the result for $x=0$ and $y=-2$ .

Calculate $\frac{30+320+24+256}{15}$ and find the product $(x-2y)(3x^{2}-2xy+2y^{2})$ .