Question 1

Divide the polynomials by using an appropriate method. $$\left( 20 r ^ { 4 } - 28 r ^ { 3 } - 38 r ^ { 2 } + 15 r + 9 \right) \div \left( - 4 r ^ { 2 } + 2 \right)$$

Accepted Answer

A)  $- 5 r ^ { 2 } + 7 r + 7 + \frac { r - 5 } { - 4 r ^ { 2 } + 2 }$ 
B)  $- 5 r ^ { 2 } + 7 r - 7 + \frac { - 6 r - 5 } { - 4 r ^ { 2 } + 2 }$ 
C)  $- 5 r ^ { 2 } + 7 r - 7$ 
D)  $- 5 r ^ { 2 } + 7 r + 7$ 
A)  $- 5 r ^ { 2 } + 7 r + 7 + \frac { r - 5 } { - 4 r ^ { 2 } + 2 }$ 
B)  $- 5 r ^ { 2 } + 7 r - 7 + \frac { - 6 r - 5 } { - 4 r ^ { 2 } + 2 }$ 
C)  $- 5 r ^ { 2 } + 7 r - 7$ 
D)  $- 5 r ^ { 2 } + 7 r + 7$

Question 2

Factor the expression that defines the function. $$g ( x ) = 5 x ^ { 2 } - 44 x - 9$$

Accepted Answer

A)  $g ( x ) = x ( 5 x - 44 ) - 9$ 
B)  $g ( x ) = ( 5 x + 1 ) ( x - 9 )$ 
C)  $g ( x ) = ( 5 x + 1 ) ( x + 9 )$ 
D)  $g ( x ) = ( 5 x - 1 ) ( x + 9 )$ 
A)  $g ( x ) = x ( 5 x - 44 ) - 9$ 
B)  $g ( x ) = ( 5 x + 1 ) ( x - 9 )$ 
C)  $g ( x ) = ( 5 x + 1 ) ( x + 9 )$ 
D)  $g ( x ) = ( 5 x - 1 ) ( x + 9 )$

Question 3

(3x + 8) multiplied by what binomial will result in the trinomial $12 x ^ { 2 } + 35 x + 8$ ?

Accepted Answer

A)  (4x + 1) 
B)  (x - 1) 
C)  (x + 1) 
D)  (4x - 1) 
A)  (4x + 1) 
B)  (x - 1) 
C)  (x + 1) 
D)  (4x - 1)

Question 4

Factor out the greatest common factor. $24 m - 24$

Accepted Answer

A)  $6 ( 4 m - 4 )$ 
B)  $24 ( m - 6 )$ 
C)  $24 ( m - 1 )$ 
D)  $4 ( 6 m - 6 )$ 
A)  $6 ( 4 m - 4 )$ 
B)  $24 ( m - 6 )$ 
C)  $24 ( m - 1 )$ 
D)  $4 ( 6 m - 6 )$

Question 5

Multiply by using the special case products. $( - 4 v + 6 w ) ^ { 2 }$

Accepted Answer

A)  $16 v ^ { 2 } + 48 v w + 36 w ^ { 2 }$ 
B)  $16 v ^ { 2 } + 36 w ^ { 2 }$ 
C)  $16 v ^ { 2 } - 48 v w + 36 w ^ { 2 }$ 
D)  $16 v ^ { 2 } - 24 v w + 36 w ^ { 2 }$ 
A)  $16 v ^ { 2 } + 48 v w + 36 w ^ { 2 }$ 
B)  $16 v ^ { 2 } + 36 w ^ { 2 }$ 
C)  $16 v ^ { 2 } - 48 v w + 36 w ^ { 2 }$ 
D)  $16 v ^ { 2 } - 24 v w + 36 w ^ { 2 }$

Question 6

Add or subtract as indicated. $\begin{array}{rr}
7.1 u^{5}+9.2 u^{2} & -1.1 u+1.6 \
+-4.7 u^{5}+5.7 u^{3} & -8.4 u-1.7 \
\hline
\end{array}$

Accepted Answer

A)  $11.8 u ^ { 5 } - 5.7 u ^ { 3 } + 9.2 u ^ { 2 } + 7.3 \mathrm { u } + 3.3$ 
B)  $2.4 u ^ { 5 } + 5.7 u ^ { 3 } + 9.2 u ^ { 2 } - 9.5 \mathrm { u } - 0.1$ 
C)  $2.4 u ^ { 5 } + 9.2 u ^ { 2 } - 9.5 \mathrm { u } - 0.1$ 
D)  $2.4 u ^ { 5 } + 1.6 u ^ { 3 } - 9.5 \mathrm { u } - 0.1$ 
A)  $11.8 u ^ { 5 } - 5.7 u ^ { 3 } + 9.2 u ^ { 2 } + 7.3 \mathrm { u } + 3.3$ 
B)  $2.4 u ^ { 5 } + 5.7 u ^ { 3 } + 9.2 u ^ { 2 } - 9.5 \mathrm { u } - 0.1$ 
C)  $2.4 u ^ { 5 } + 9.2 u ^ { 2 } - 9.5 \mathrm { u } - 0.1$ 
D)  $2.4 u ^ { 5 } + 1.6 u ^ { 3 } - 9.5 \mathrm { u } - 0.1$

Question 7

Subtract the polynomials and simplify. $$\left( - \frac { 2 } { 5 } p ^ { 2 } - \frac { 1 } { 15 } p q + \frac { 4 } { 15 } q ^ { 2 } - 8 \right) - \left( \frac { 14 } { 15 } p ^ { 2 } + \frac { 2 } { 15 } p q + \frac { 1 } { 5 } q ^ { 2 } + 14 \right)$$

Accepted Answer

A)  $- \frac { 4 } { 3 } p ^ { 2 } - \frac { 1 } { 5 } p q + \frac { 1 } { 15 } q ^ { 2 } - 22$ 
B)  $- \frac { 4 } { 3 } p ^ { 2 } + \frac { 1 } { 15 } p q + \frac { 7 } { 15 } q ^ { 2 } + 6$ 
C)  $- \frac { 4 } { 3 } p ^ { 2 } - \frac { 1 } { 5 } p q + \frac { 1 } { 15 } q ^ { 2 } + 6$ 
D)  $\frac { 8 } { 15 } p ^ { 2 } + \frac { 1 } { 15 } p q + \frac { 7 } { 15 } q ^ { 2 } + 6$ 
A)  $- \frac { 4 } { 3 } p ^ { 2 } - \frac { 1 } { 5 } p q + \frac { 1 } { 15 } q ^ { 2 } - 22$ 
B)  $- \frac { 4 } { 3 } p ^ { 2 } + \frac { 1 } { 15 } p q + \frac { 7 } { 15 } q ^ { 2 } + 6$ 
C)  $- \frac { 4 } { 3 } p ^ { 2 } - \frac { 1 } { 5 } p q + \frac { 1 } { 15 } q ^ { 2 } + 6$ 
D)  $\frac { 8 } { 15 } p ^ { 2 } + \frac { 1 } { 15 } p q + \frac { 7 } { 15 } q ^ { 2 } + 6$

Question 8

Choose the polynomial that is described. A trinomial in one variable of degree 3

Accepted Answer

A)  $- 8 a ^ { 3 }$ 
B)  $3 a ^ { 3 } + 3 a ^ { 2 } + 3 a + 3$ 
C)  $- 8 a ^ { 3 } - 8 a ^ { 2 } + 7 a + 8$ 
D)  $- 8 a ^ { 3 } + 7 a + 8$ 
A)  $- 8 a ^ { 3 }$ 
B)  $3 a ^ { 3 } + 3 a ^ { 2 } + 3 a + 3$ 
C)  $- 8 a ^ { 3 } - 8 a ^ { 2 } + 7 a + 8$ 
D)  $- 8 a ^ { 3 } + 7 a + 8$

Question 9

Divide the polynomials by using long division. $$\left( x ^ { 3 } - 5 x ^ { 2 } - 2 x + 14 \right) \div ( x - 1 )$$

Accepted Answer

A)  $x ^ { 2 } - 6 x + 4 + \frac { 14 } { x - 1 }$ 
B)  $x ^ { 2 } - 4 x - 6 + \frac { 1 } { x - 1 }$ 
C)  $x ^ { 2 } - 4 x - 6 + \frac { 8 } { x - 1 }$ 
D)  $x ^ { 2 } - 4 x + 6 + \frac { 20 } { x - 1 }$ 
A)  $x ^ { 2 } - 6 x + 4 + \frac { 14 } { x - 1 }$ 
B)  $x ^ { 2 } - 4 x - 6 + \frac { 1 } { x - 1 }$ 
C)  $x ^ { 2 } - 4 x - 6 + \frac { 8 } { x - 1 }$ 
D)  $x ^ { 2 } - 4 x + 6 + \frac { 20 } { x - 1 }$

Question 10

Factor the sum or difference of cubes. $250 s ^ { 4 } + 16 s$

Accepted Answer

A)  $2 s \left( 125 s ^ { 3 } + 8 \right)$ 
B)  $2 \left( 125 s ^ { 4 } + 8 s \right)$ 
C)  $2 \left( s ^ { 2 } - 2 \right) \left( s ^ { 2 } + 4 \right)$ 
D)  $2 s ( 5 s + 2 ) \left( 25 s ^ { 2 } - 10 s + 4 \right)$ 
A)  $2 s \left( 125 s ^ { 3 } + 8 \right)$ 
B)  $2 \left( 125 s ^ { 4 } + 8 s \right)$ 
C)  $2 \left( s ^ { 2 } - 2 \right) \left( s ^ { 2 } + 4 \right)$ 
D)  $2 s ( 5 s + 2 ) \left( 25 s ^ { 2 } - 10 s + 4 \right)$

Question 11

Factor completely using the difference of squares along with factoring by grouping. $9 x ^ { 3 } + 7 x ^ { 2 } - 36 x - 28$

Accepted Answer

A)  $( 9 x - 7 ) ( x + 2 ) ( x - 2 )$ 
B)  $( 9 x - 7 ) ( x - 2 ) ^ { 2 }$ 
C)  $( 9 x + 7 ) ( x - 2 ) ^ { 2 }$ 
D)  $( 9 x + 7 ) ( x + 2 ) ( x - 2 )$ 
A)  $( 9 x - 7 ) ( x + 2 ) ( x - 2 )$ 
B)  $( 9 x - 7 ) ( x - 2 ) ^ { 2 }$ 
C)  $( 9 x + 7 ) ( x - 2 ) ^ { 2 }$ 
D)  $( 9 x + 7 ) ( x + 2 ) ( x - 2 )$

Question 12

Factor the trinomial completely by using any method. Remember to look for a common factor first. $4 t ^ { 3 } - 40 t ^ { 2 } u + 100 t u ^ { 2 }$

Accepted Answer

A)  Prime 
B)  $4 t ^ { 2 } ( 1 - 5 u ) ^ { 2 }$ 
C)  $4 t ( t - 5 u ) ( t + 5 u )$ 
D)  $4 t ( t - 5 u ) ^ { 2 }$ 
A)  Prime 
B)  $4 t ^ { 2 } ( 1 - 5 u ) ^ { 2 }$ 
C)  $4 t ( t - 5 u ) ( t + 5 u )$ 
D)  $4 t ( t - 5 u ) ^ { 2 }$

Question 13

Write an expression for the area and simplify your answer.  
[The figure is not necessarily drawn to scale.]

Accepted Answer

A)  $72 x ^ { 2 } + 86 x - 24$ 
B)  $72 x ^ { 2 } + 22 x - 24$ 
C)  $36 x ^ { 2 } + 43 x - 12$ 
D)  $36 x ^ { 2 } + 11 x - 12$ 
A)  $72 x ^ { 2 } + 86 x - 24$ 
B)  $72 x ^ { 2 } + 22 x - 24$ 
C)  $36 x ^ { 2 } + 43 x - 12$ 
D)  $36 x ^ { 2 } + 11 x - 12$

Question 14

Solve the equation. $$0 = 3 ( s + 6.7 ) ( s + 5.5 )$$

Accepted Answer

A)  $s = - 6.7 ; s = - 5.5$ 
B)  $s = 3 ; s = 6.7 ; s = 5.5$ 
C)  $s = - 6.7 ; s = 5.5$ 
D)  $s = 6.7 ; s = 5.5$ 
A)  $s = - 6.7 ; s = - 5.5$ 
B)  $s = 3 ; s = 6.7 ; s = 5.5$ 
C)  $s = - 6.7 ; s = 5.5$ 
D)  $s = 6.7 ; s = 5.5$

Question 15

Find the perimeter.

Accepted Answer

A)  $40 x - 10$ 
B)  $20 x - 3$ 
C)  $20 x - 5$ 
D)  $12 x - 3$ 
A)  $40 x - 10$ 
B)  $20 x - 3$ 
C)  $20 x - 5$ 
D)  $12 x - 3$

Question 16

Factor the expression that defines the function. $$n ( t ) = t ^ { 2 } - 18 t + 81$$

Accepted Answer

A)  $n ( t ) = \left( t - \frac { 9 } { 2 } \right) ^ { 2 }$ 
B)  $n ( t ) = ( t - 9 ) ( t + 9 )$ 
C)  $n ( t ) = ( t - 9 ) ^ { 2 }$ 
D)  $n ( t ) = t ^ { 2 } - 18 t + 81$ (Expression is prime) 
A)  $n ( t ) = \left( t - \frac { 9 } { 2 } \right) ^ { 2 }$ 
B)  $n ( t ) = ( t - 9 ) ( t + 9 )$ 
C)  $n ( t ) = ( t - 9 ) ^ { 2 }$ 
D)  $n ( t ) = t ^ { 2 } - 18 t + 81$ (Expression is prime)

Question 17

The cost in dollars of producing x fruit baskets is C(x) = 8.5x + 10. The revenue received is R(x) = 24.95x. The profit is the revenue minus the cost. Write and simplify a function P that Represents the profit.

Accepted Answer

A)  P(x) = -16.45x - 10 
B)  P(x) = 16.45x - 10 
C)  P(x) = 16.45x + 10 
D)  P(x) = 33.45x + 10 
A)  P(x) = -16.45x - 10 
B)  P(x) = 16.45x - 10 
C)  P(x) = 16.45x + 10 
D)  P(x) = 33.45x + 10

Question 18

Factor completely. $64 m ^ { 6 } - n ^ { 6 } \quad$ [Hint: $64 = 2 ^ { 6 }$.]

Accepted Answer

A)  $( 2 m - n ) \left( 4 m ^ { 2 } + 2 m n + n ^ { 2 } \right) \left( 8 m ^ { 3 } + n ^ { 3 } \right)$ 
B)  $( 2 m + n ) \left( 4 m ^ { 2 } - 2 m n + n ^ { 2 } \right) ( 2 m - n ) \left( 4 m ^ { 2 } + 2 m n + n ^ { 2 } \right)$ 
C)  $\left( 8 m ^ { 3 } - n ^ { 3 } \right) \left( 8 m ^ { 3 } + n ^ { 3 } \right)$ 
D)  Prime 
A)  $( 2 m - n ) \left( 4 m ^ { 2 } + 2 m n + n ^ { 2 } \right) \left( 8 m ^ { 3 } + n ^ { 3 } \right)$ 
B)  $( 2 m + n ) \left( 4 m ^ { 2 } - 2 m n + n ^ { 2 } \right) ( 2 m - n ) \left( 4 m ^ { 2 } + 2 m n + n ^ { 2 } \right)$ 
C)  $\left( 8 m ^ { 3 } - n ^ { 3 } \right) \left( 8 m ^ { 3 } + n ^ { 3 } \right)$ 
D)  Prime

Question 19

Divide the polynomials. $$\left( - 16 m ^ { 5 } n - 32 m ^ { 4 } n + 6 m ^ { 3 } n \right) \div \left( 8 m ^ { 3 } n \right)$$

Accepted Answer

A)  $- 2 m ^ { 2 } - 4 m + \frac { 3 } { 4 }$ 
B)  $- 2 m ^ { 2 } - 4 m n + \frac { 3 } { 4 } n$ 
C)  $- 2 m ^ { 2 } - 32 m ^ { 4 } n + 6 m ^ { 3 } n$ 
D)  $- 2 m ^ { 2 } - 4 m ^ { 2 } + \frac { 3 } { 4 }$ 
A)  $- 2 m ^ { 2 } - 4 m + \frac { 3 } { 4 }$ 
B)  $- 2 m ^ { 2 } - 4 m n + \frac { 3 } { 4 } n$ 
C)  $- 2 m ^ { 2 } - 32 m ^ { 4 } n + 6 m ^ { 3 } n$ 
D)  $- 2 m ^ { 2 } - 4 m ^ { 2 } + \frac { 3 } { 4 }$

Question 20

Find the x- and y-intercepts for the function defined by y = f (x). $$f ( x ) = ( x - 1 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$$

Accepted Answer

A)  $x$-intercepts: $( 1,0 ) , ( - 4,0 ) , ( - 5,0 ) ; y$-intercept: none 
B)  $x$-intercepts: $( - 1,0 ) , ( 4,0 ) , ( 5,0 ) ; y$-intercept: none 
C)  $x$-intercepts: $( - 1,0 ) , ( 4,0 ) , ( 5,0 ) ; y$-intercept: $( 0 , - 100 )$ 
D)  $x$-intercepts: $( 1,0 ) , ( - 4,0 ) , ( - 5,0 ) ; y$-intercept: $( 0 , - 100 )$ 
A)  $x$-intercepts: $( 1,0 ) , ( - 4,0 ) , ( - 5,0 ) ; y$-intercept: none 
B)  $x$-intercepts: $( - 1,0 ) , ( 4,0 ) , ( 5,0 ) ; y$-intercept: none 
C)  $x$-intercepts: $( - 1,0 ) , ( 4,0 ) , ( 5,0 ) ; y$-intercept: $( 0 , - 100 )$ 
D)  $x$-intercepts: $( 1,0 ) , ( - 4,0 ) , ( - 5,0 ) ; y$-intercept: $( 0 , - 100 )$

Divide the polynomials by using an appropriate method. $\left( 20 r ^ { 4 } - 28 r ^ { 3 } - 38 r ^ { 2 } + 15 r + 9 \right) \div \left( - 4 r ^ { 2 } + 2 \right)$

Factor the expression that defines the function. $g ( x ) = 5 x ^ { 2 } - 44 x - 9$

(3x + 8) multiplied by what binomial will result in the trinomial $12 x ^ { 2 } + 35 x + 8$ ?

Factor out the greatest common factor. $24 m - 24$

Multiply by using the special case products. $( - 4 v + 6 w ) ^ { 2 }$

Add or subtract as indicated. 7.1+9.2 -1.1u+1.6 +-4.7+5.7 -8.4u-1.7

Subtract the polynomials and simplify. $\left( - \frac { 2 } { 5 } p ^ { 2 } - \frac { 1 } { 15 } p q + \frac { 4 } { 15 } q ^ { 2 } - 8 \right) - \left( \frac { 14 } { 15 } p ^ { 2 } + \frac { 2 } { 15 } p q + \frac { 1 } { 5 } q ^ { 2 } + 14 \right)$

Choose the polynomial that is described. A trinomial in one variable of degree 3

Divide the polynomials by using long division. $\left( x ^ { 3 } - 5 x ^ { 2 } - 2 x + 14 \right) \div ( x - 1 )$

Factor the sum or difference of cubes. $250 s ^ { 4 } + 16 s$

Factor completely using the difference of squares along with factoring by grouping. $9 x ^ { 3 } + 7 x ^ { 2 } - 36 x - 28$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $4 t ^ { 3 } - 40 t ^ { 2 } u + 100 t u ^ { 2 }$

Write an expression for the area and simplify your answer. [The figure is not necessarily drawn to scale.]

Solve the equation. $0 = 3 ( s + 6.7 ) ( s + 5.5 )$

Find the perimeter.

Factor the expression that defines the function. $n ( t ) = t ^ { 2 } - 18 t + 81$

The cost in dollars of producing x fruit baskets is C(x) = 8.5x + 10. The revenue received is R(x) = 24.95x. The profit is the revenue minus the cost. Write and simplify a function P that Represents the profit.

Factor completely. $64 m ^ { 6 } - n ^ { 6 } \quad$ [Hint: $64 = 2 ^ { 6 }$ .]

Divide the polynomials. $\left( - 16 m ^ { 5 } n - 32 m ^ { 4 } n + 6 m ^ { 3 } n \right) \div \left( 8 m ^ { 3 } n \right)$

Find the x- and y-intercepts for the function defined by y = f (x). $f ( x ) = ( x - 1 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Exam 4: Polynomials

Divide the polynomials by using an appropriate method. (20r4−28r3−38r2+15r+9)÷(−4r2+2)\left( 20 r ^ { 4 } - 28 r ^ { 3 } - 38 r ^ { 2 } + 15 r + 9 \right) \div \left( - 4 r ^ { 2 } + 2 \right)(20r4−28r3−38r2+15r+9)÷(−4r2+2)

Factor the expression that defines the function. g(x)=5x2−44x−9g ( x ) = 5 x ^ { 2 } - 44 x - 9g(x)=5x2−44x−9

(3x + 8) multiplied by what binomial will result in the trinomial 12x2+35x+812 x ^ { 2 } + 35 x + 812x2+35x+8 ?

Factor out the greatest common factor. 24m−2424 m - 2424m−24

Multiply by using the special case products. (−4v+6w)2( - 4 v + 6 w ) ^ { 2 }(−4v+6w)2

Add or subtract as indicated. 7.1+9.2 -1.1u+1.6 +-4.7+5.7 -8.4u-1.7

Choose the polynomial that is described. A trinomial in one variable of degree 3

Divide the polynomials by using long division. (x3−5x2−2x+14)÷(x−1)\left( x ^ { 3 } - 5 x ^ { 2 } - 2 x + 14 \right) \div ( x - 1 )(x3−5x2−2x+14)÷(x−1)

Factor the sum or difference of cubes. 250s4+16s250 s ^ { 4 } + 16 s250s4+16s

Factor completely using the difference of squares along with factoring by grouping. 9x3+7x2−36x−289 x ^ { 3 } + 7 x ^ { 2 } - 36 x - 289x3+7x2−36x−28

Factor the trinomial completely by using any method. Remember to look for a common factor first. 4t3−40t2u+100tu24 t ^ { 3 } - 40 t ^ { 2 } u + 100 t u ^ { 2 }4t3−40t2u+100tu2

Write an expression for the area and simplify your answer. [The figure is not necessarily drawn to scale.]

Solve the equation. 0=3(s+6.7)(s+5.5)0 = 3 ( s + 6.7 ) ( s + 5.5 )0=3(s+6.7)(s+5.5)

Find the perimeter.

Factor the expression that defines the function. n(t)=t2−18t+81n ( t ) = t ^ { 2 } - 18 t + 81n(t)=t2−18t+81

The cost in dollars of producing x fruit baskets is C(x) = 8.5x + 10. The revenue received is R(x) = 24.95x. The profit is the revenue minus the cost. Write and simplify a function P that Represents the profit.

Factor completely. 64m6−n664 m ^ { 6 } - n ^ { 6 } \quad64m6−n6 [Hint: 64=2664 = 2 ^ { 6 }64=26 .]

Divide the polynomials. (−16m5n−32m4n+6m3n)÷(8m3n)\left( - 16 m ^ { 5 } n - 32 m ^ { 4 } n + 6 m ^ { 3 } n \right) \div \left( 8 m ^ { 3 } n \right)(−16m5n−32m4n+6m3n)÷(8m3n)

Find the x- and y-intercepts for the function defined by y = f (x). f(x)=(x−1)(x+4)(x+5)2f ( x ) = ( x - 1 ) ( x + 4 ) ( x + 5 ) ^ { 2 }f(x)=(x−1)(x+4)(x+5)2

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Divide the polynomials by using an appropriate method. $\left( 20 r ^ { 4 } - 28 r ^ { 3 } - 38 r ^ { 2 } + 15 r + 9 \right) \div \left( - 4 r ^ { 2 } + 2 \right)$

Factor the expression that defines the function. $g ( x ) = 5 x ^ { 2 } - 44 x - 9$

(3x + 8) multiplied by what binomial will result in the trinomial $12 x ^ { 2 } + 35 x + 8$ ?

Factor out the greatest common factor. $24 m - 24$

Multiply by using the special case products. $( - 4 v + 6 w ) ^ { 2 }$

Divide the polynomials by using long division. $\left( x ^ { 3 } - 5 x ^ { 2 } - 2 x + 14 \right) \div ( x - 1 )$

Factor the sum or difference of cubes. $250 s ^ { 4 } + 16 s$

Factor completely using the difference of squares along with factoring by grouping. $9 x ^ { 3 } + 7 x ^ { 2 } - 36 x - 28$

Factor the trinomial completely by using any method. Remember to look for a common factor first. $4 t ^ { 3 } - 40 t ^ { 2 } u + 100 t u ^ { 2 }$

Solve the equation. $0 = 3 ( s + 6.7 ) ( s + 5.5 )$

Factor the expression that defines the function. $n ( t ) = t ^ { 2 } - 18 t + 81$

Factor completely. $64 m ^ { 6 } - n ^ { 6 } \quad$ [Hint: $64 = 2 ^ { 6 }$ .]

Divide the polynomials. $\left( - 16 m ^ { 5 } n - 32 m ^ { 4 } n + 6 m ^ { 3 } n \right) \div \left( 8 m ^ { 3 } n \right)$

Find the x- and y-intercepts for the function defined by y = f (x). $f ( x ) = ( x - 1 ) ( x + 4 ) ( x + 5 ) ^ { 2 }$