Question 1

Find the sum $\left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right) + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right)$ .

Accepted Answer

A)  $\frac { 15 } { 16 } x ^ { 3 } - 3$ 
B)  $\frac { 15 } { 16 } x ^ { 6 } - 3$ 
C)  $15 x ^ { 3 } - 48$ 
D)  $15 x ^ { 6 } - 48$ 
E)  $\frac { 15 } { 16 } x ^ { 9 } - 3$ 
A)  $\frac { 15 } { 16 } x ^ { 3 } - 3$ 
B)  $\frac { 15 } { 16 } x ^ { 6 } - 3$ 
C)  $15 x ^ { 3 } - 48$ 
D)  $15 x ^ { 6 } - 48$ 
E)  $\frac { 15 } { 16 } x ^ { 9 } - 3$

Question 2

Solve the equation below by factoring. $$x ^ { 4 } - 2 x ^ { 3 } - 16 x ^ { 2 } + 32 x = 0$$

Accepted Answer

A)  $4,0,2$ 
B)  $\pm 4,0,2$ 
C)  $- 8,0,4$ 
D)  $\pm 4 , \pm 2$ 
E)  $\pm 8,4$ 
A)  $4,0,2$ 
B)  $\pm 4,0,2$ 
C)  $- 8,0,4$ 
D)  $\pm 4 , \pm 2$ 
E)  $\pm 8,4$

Question 3

Find an expression for the perimeter of the figure. Assume all angles are right angles.

Accepted Answer

A)  52z 
B)  24z+4 
C)  108 z2+12 z 
D)  48z+4 
E)  28z 
A)  52z 
B)  24z+4 
C)  108 z2+12 z 
D)  48z+4 
E)  28z

Question 4

Find two real numbers b such that the expression $x ^ { 2 } + b x + 196$ is a perfect square trinomial.

Accepted Answer

A)  $\pm 14$ 
B)  $\pm 15$ 
C)  $\pm 42$ 
D)  $\pm 196$ 
E)  $\pm 28$ 
A)  $\pm 14$ 
B)  $\pm 15$ 
C)  $\pm 42$ 
D)  $\pm 196$ 
E)  $\pm 28$

Question 5

Subtract $3 y ^ { 2 } - 3 y ^ { 3 } \text { from } 9 y ^ { 5 } + 9 y ^ { 3 }$ .

Accepted Answer

A)  $6 y ^ { 3 } + 12$ 
B)  $- 9 y ^ { 5 } - 12 y ^ { 3 } + 3 y ^ { 2 }$ 
C)  $- 6 y ^ { 3 } - 12$ 
D)  $9 y ^ { 5 } + 12 y ^ { 3 } - 3 y ^ { 2 }$ 
E)  $6 y ^ { 5 } + 12 y ^ { 3 }$ 
A)  $6 y ^ { 3 } + 12$ 
B)  $- 9 y ^ { 5 } - 12 y ^ { 3 } + 3 y ^ { 2 }$ 
C)  $- 6 y ^ { 3 } - 12$ 
D)  $9 y ^ { 5 } + 12 y ^ { 3 } - 3 y ^ { 2 }$ 
E)  $6 y ^ { 5 } + 12 y ^ { 3 }$

Question 6

Find $h ( x ) = f ( x ) + g ( x )$ where $f ( x ) = 8 x ^ { 3 } - 9 x ^ { 2 } + 8$ and $g ( x ) = 10 - x - x ^ { 2 } - 9 x ^ { 3 }$

Accepted Answer

A)  $h ( x ) = - x ^ { 3 } - 10 x ^ { 2 } - x + 18$ 
B)  $h ( x ) = - x ^ { 6 } - 8 x ^ { 2 } - x - 2$ 
C)  $h ( x ) = 17 x ^ { 3 } - 8 x ^ { 2 } - x - 2$ 
D)  $h ( x ) = - 17 x ^ { 3 } - 8 x ^ { 2 } - x - 2$ 
E)  $h ( x ) = - x ^ { 3 } - 10 x ^ { 2 } + x + 18$ 
A)  $h ( x ) = - x ^ { 3 } - 10 x ^ { 2 } - x + 18$ 
B)  $h ( x ) = - x ^ { 6 } - 8 x ^ { 2 } - x - 2$ 
C)  $h ( x ) = 17 x ^ { 3 } - 8 x ^ { 2 } - x - 2$ 
D)  $h ( x ) = - 17 x ^ { 3 } - 8 x ^ { 2 } - x - 2$ 
E)  $h ( x ) = - x ^ { 3 } - 10 x ^ { 2 } + x + 18$

Question 7

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+5 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box if dimensions increase by 6 inches.

Accepted Answer

A)  $A ( n ) = n ^ { 2 } + 4 n - 116$ 
B)  $A ( n ) = n ^ { 2 } - 11 n + 110$ 
C)  $A ( n ) = n ^ { 2 } + 4 n + 110$ 
D)  $A ( n ) = n ^ { 2 } + 21 n + 110$ 
E)  $A ( n ) = n ^ { 2 } + 11 n + 110$ 
A)  $A ( n ) = n ^ { 2 } + 4 n - 116$ 
B)  $A ( n ) = n ^ { 2 } - 11 n + 110$ 
C)  $A ( n ) = n ^ { 2 } + 4 n + 110$ 
D)  $A ( n ) = n ^ { 2 } + 21 n + 110$ 
E)  $A ( n ) = n ^ { 2 } + 11 n + 110$

Question 8

Find the sum $( 6 x + 2 ) + ( 8 x - 6 )$.

Accepted Answer

A)  $48 x - 4$ 
B)  10x 
C)  14x-4 
D)  $14 x ^ { 2 } - 4$ 
E)  $10 x ^ { 2 }$ 
A)  $48 x - 4$ 
B)  10x 
C)  14x-4 
D)  $14 x ^ { 2 } - 4$ 
E)  $10 x ^ { 2 }$

Question 9

Factor the trinomial $t ^ { 2 } - 6 t - 7$ .

Accepted Answer

A)  $( t - 7 ) ( t - 1 )$ 
B)  $( t - 7 ) ( t + 7 )$ 
C)  $( t + 7 ) ( t - 1 )$ 
D)  $( t - 1 ) ( t + 1 )$ 
E)  $( t - 7 ) ( t + 1 )$ 
A)  $( t - 7 ) ( t - 1 )$ 
B)  $( t - 7 ) ( t + 7 )$ 
C)  $( t + 7 ) ( t - 1 )$ 
D)  $( t - 1 ) ( t + 1 )$ 
E)  $( t - 7 ) ( t + 1 )$

Question 10

Find the greatest common factor of the expressions $7 ( x - 4 ) ^ { 2 }$ and $7 ( x - 4 ) ^ { 3 }$ .

Accepted Answer

A)  $7 ( x - 4 ) ^ { 2 }$ 
B)  $49 ( x - 4 ) ^ { 3 }$ 
C)  $49 ( x - 4 ) ^ { 5 }$ 
D)  $7 ( x - 4 ) ^ { 3 }$ 
E)  $49 ( x - 4 ) ^ { 2 }$ 
A)  $7 ( x - 4 ) ^ { 2 }$ 
B)  $49 ( x - 4 ) ^ { 3 }$ 
C)  $49 ( x - 4 ) ^ { 5 }$ 
D)  $7 ( x - 4 ) ^ { 3 }$ 
E)  $49 ( x - 4 ) ^ { 2 }$

Question 11

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n } y ^ { 3 xn - 1 } } { x ^ { n } y ^ { n - 4 } }$

Accepted Answer

A)  $x ^ { 3 } y ^ { 2 }$ 
B)  $x ^ { 3 } y ^ { 2 n + 3 }$ 
C)  $x ^ { 3 n } y ^ { 2 n + 3 }$ 
D)  $x ^ { 2 } y ^ { 2 n + 3 }$ 
E)  $x ^ { 2 n } y ^ { 2 n + 3 }$ 
A)  $x ^ { 3 } y ^ { 2 }$ 
B)  $x ^ { 3 } y ^ { 2 n + 3 }$ 
C)  $x ^ { 3 n } y ^ { 2 n + 3 }$ 
D)  $x ^ { 2 } y ^ { 2 n + 3 }$ 
E)  $x ^ { 2 n } y ^ { 2 n + 3 }$

Question 12

Multiply: $- 9 u \left( - 5 u ^ { 2 } + 2 \right)$

Accepted Answer

A)  $45 u ^ { 2 } - 18$ 
B)  $45 u ^ { 3 } + 2$ 
C)  $45 u ^ { 2 } + 2 u$ 
D)  $45 u ^ { 3 } - 18$ 
E)  $45 u ^ { 3 } - 18 u$ 
A)  $45 u ^ { 2 } - 18$ 
B)  $45 u ^ { 3 } + 2$ 
C)  $45 u ^ { 2 } + 2 u$ 
D)  $45 u ^ { 3 } - 18$ 
E)  $45 u ^ { 3 } - 18 u$

Question 13

Multiply the polynomials and simplify. $\begin{array} { r } 
x ^ { 2 } + 5 x - 6 \
\times \quad 3 x + 4 \
\hline
\end{array}$

Accepted Answer

A)  $3 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 6$ 
B)  $3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 24$ 
C)  $3 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 24$ 
D)  $3 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 6$ 
E)  $3 x ^ { 3 } + 20 x ^ { 2 } - 6$ 
A)  $3 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 6$ 
B)  $3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 24$ 
C)  $3 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 24$ 
D)  $3 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 6$ 
E)  $3 x ^ { 3 } + 20 x ^ { 2 } - 6$

Question 14

Factor the expression by factoring out the common binomial factor. $( 2 x - 3 ) ( x + 5 ) + ( 7 x + 1 ) ( x + 5 )$

Accepted Answer

A)  $( 9 x - 2 ) ( 2 x - 3 )$ 
B)  $( 2 x - 3 ) ( 7 x + 1 )$ 
C)  $( 7 x + 1 ) ( x + 5 )$ 
D)  $( 9 x - 2 ) ( x + 5 )$ 
E)  $( 2 x - 3 ) ( x + 5 )$ 
A)  $( 9 x - 2 ) ( 2 x - 3 )$ 
B)  $( 2 x - 3 ) ( 7 x + 1 )$ 
C)  $( 7 x + 1 ) ( x + 5 )$ 
D)  $( 9 x - 2 ) ( x + 5 )$ 
E)  $( 2 x - 3 ) ( x + 5 )$

Question 15

Use a graphing calculator to find any x -intercepts of the graph $y = 7 x ^ { 3 } - 95 x ^ { 2 } - 42 x$ .

Accepted Answer

A)  $\left( \frac { 3 } { 7 } , 0 \right) , ( - 14,0 )$ 
B)  $\left( \frac { 7 } { 3 } , 0 \right) , ( 0,0 ) , ( - 7,0 )$ 
C)  $\left( - \frac { 3 } { 7 } , 0 \right) , ( 0,0 ) , ( - 7,0 )$ 
D)  $\left( - \frac { 3 } { 7 } , 0 \right) , ( 0,0 ) , ( 14,0 )$ 
E)  $\left( - \frac { 7 } { 3 } , 0 \right) , ( 14,0 )$ 
A)  $\left( \frac { 3 } { 7 } , 0 \right) , ( - 14,0 )$ 
B)  $\left( \frac { 7 } { 3 } , 0 \right) , ( 0,0 ) , ( - 7,0 )$ 
C)  $\left( - \frac { 3 } { 7 } , 0 \right) , ( 0,0 ) , ( - 7,0 )$ 
D)  $\left( - \frac { 3 } { 7 } , 0 \right) , ( 0,0 ) , ( 14,0 )$ 
E)  $\left( - \frac { 7 } { 3 } , 0 \right) , ( 14,0 )$

Question 16

Factor the expression $( x + 4 y ) ^ { 2 } - 9 a ^ { 2 }$ completely.

Accepted Answer

A)  $( x + 4 y + 3 a ) ( x - 4 y - 3 a )$ 
B)  $( x + 4 y - 3 a ) ^ { 2 }$ 
C)  $( x + 4 y + 3 a ) ^ { 2 }$ 
D)  $( x + 4 y + 9 a ) ( x + 4 y - 9 a )$ 
E)  $( x + 4 y + 3 a ) ( x + 4 y - 3 a )$ 
A)  $( x + 4 y + 3 a ) ( x - 4 y - 3 a )$ 
B)  $( x + 4 y - 3 a ) ^ { 2 }$ 
C)  $( x + 4 y + 3 a ) ^ { 2 }$ 
D)  $( x + 4 y + 9 a ) ( x + 4 y - 9 a )$ 
E)  $( x + 4 y + 3 a ) ( x + 4 y - 3 a )$

Question 17

Find the greatest common factor of the expressions $15 a b ^ { 2 }$ and $45 a ^ { 2 } b ^ { 3 }$ .

Accepted Answer

A)  $15 a b ^ { 2 }$ 
B)  $675 a b ^ { 2 }$ 
C)  $675 a ^ { 3 } b ^ { 5 }$ 
D)  $15 a ^ { 3 } b ^ { 5 }$ 
E)  $675 a ^ { 2 } b ^ { 3 }$ 
A)  $15 a b ^ { 2 }$ 
B)  $675 a b ^ { 2 }$ 
C)  $675 a ^ { 3 } b ^ { 5 }$ 
D)  $15 a ^ { 3 } b ^ { 5 }$ 
E)  $675 a ^ { 2 } b ^ { 3 }$

Question 18

Use the Zero-Factor Property to solve the equation below. $28 ( a + 5 ) ( a - 7 ) = 0$

Accepted Answer

A)  $5 , - 7$ 
B)  $- 5,7$ 
C)  $28,7$ 
D)  $28 , - 5$ 
E)  $5,7$ 
A)  $5 , - 7$ 
B)  $- 5,7$ 
C)  $28,7$ 
D)  $28 , - 5$ 
E)  $5,7$

Find the sum $\left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right) + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right)$ .

Solve the equation below by factoring. $x ^ { 4 } - 2 x ^ { 3 } - 16 x ^ { 2 } + 32 x = 0$

Find an expression for the perimeter of the figure. Assume all angles are right angles.

Find two real numbers b such that the expression $x ^ { 2 } + b x + 196$ is a perfect square trinomial.

Subtract $3 y ^ { 2 } - 3 y ^ { 3 } \text { from } 9 y ^ { 5 } + 9 y ^ { 3 }$ .

Find $h ( x ) = f ( x ) + g ( x )$ where $f ( x ) = 8 x ^ { 3 } - 9 x ^ { 2 } + 8$ and $g ( x ) = 10 - x - x ^ { 2 } - 9 x ^ { 3 }$

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+5 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box if dimensions increase by 6 inches.

Find the sum $( 6 x + 2 ) + ( 8 x - 6 )$ .

Factor the trinomial $t ^ { 2 } - 6 t - 7$ .

Find the greatest common factor of the expressions $7 ( x - 4 ) ^ { 2 }$ and $7 ( x - 4 ) ^ { 3 }$ .

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n } y ^ { 3 xn - 1 } } { x ^ { n } y ^ { n - 4 } }$

Multiply: $- 9 u \left( - 5 u ^ { 2 } + 2 \right)$

Multiply the polynomials and simplify. +5x-6 \times3x+4

Factor the expression by factoring out the common binomial factor. $( 2 x - 3 ) ( x + 5 ) + ( 7 x + 1 ) ( x + 5 )$

Use a graphing calculator to find any x -intercepts of the graph $y = 7 x ^ { 3 } - 95 x ^ { 2 } - 42 x$ .

Factor the expression $( x + 4 y ) ^ { 2 } - 9 a ^ { 2 }$ completely.

Find the greatest common factor of the expressions $15 a b ^ { 2 }$ and $45 a ^ { 2 } b ^ { 3 }$ .

Use the Zero-Factor Property to solve the equation below. $28 ( a + 5 ) ( a - 7 ) = 0$

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Polynomials and Factoring

Find the sum (58x3+2)+(516x3−5)\left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right) + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right)(85​x3+2)+(165​x3−5) .

Solve the equation below by factoring. x4−2x3−16x2+32x=0x ^ { 4 } - 2 x ^ { 3 } - 16 x ^ { 2 } + 32 x = 0x4−2x3−16x2+32x=0

Find an expression for the perimeter of the figure. Assume all angles are right angles.

Find two real numbers b such that the expression x2+bx+196x ^ { 2 } + b x + 196x2+bx+196 is a perfect square trinomial.

Subtract 3y2−3y3 from 9y5+9y33 y ^ { 2 } - 3 y ^ { 3 } \text { from } 9 y ^ { 5 } + 9 y ^ { 3 }3y2−3y3 from 9y5+9y3 .

Find h(x)=f(x)+g(x)h ( x ) = f ( x ) + g ( x )h(x)=f(x)+g(x) where f(x)=8x3−9x2+8f ( x ) = 8 x ^ { 3 } - 9 x ^ { 2 } + 8f(x)=8x3−9x2+8 and g(x)=10−x−x2−9x3g ( x ) = 10 - x - x ^ { 2 } - 9 x ^ { 3 }g(x)=10−x−x2−9x3

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+5 inches. Write a polynomial function A(n)A ( n )A(n) for the area of the largest side of the box if dimensions increase by 6 inches.

Find the sum (6x+2)+(8x−6)( 6 x + 2 ) + ( 8 x - 6 )(6x+2)+(8x−6) .

Factor the trinomial t2−6t−7t ^ { 2 } - 6 t - 7t2−6t−7 .

Find the greatest common factor of the expressions 7(x−4)27 ( x - 4 ) ^ { 2 }7(x−4)2 and 7(x−4)37 ( x - 4 ) ^ { 3 }7(x−4)3 .

Use the rules of exponents to simplify the expression below. x4ny3xn−1xnyn−4\frac { x ^ { 4 n } y ^ { 3 xn - 1 } } { x ^ { n } y ^ { n - 4 } }xnyn−4x4ny3xn−1​

Multiply: −9u(−5u2+2)- 9 u \left( - 5 u ^ { 2 } + 2 \right)−9u(−5u2+2)

Multiply the polynomials and simplify. +5x-6 \times3x+4

Factor the expression by factoring out the common binomial factor. (2x−3)(x+5)+(7x+1)(x+5)( 2 x - 3 ) ( x + 5 ) + ( 7 x + 1 ) ( x + 5 )(2x−3)(x+5)+(7x+1)(x+5)

Use a graphing calculator to find any x -intercepts of the graph y=7x3−95x2−42xy = 7 x ^ { 3 } - 95 x ^ { 2 } - 42 xy=7x3−95x2−42x .

Factor the expression (x+4y)2−9a2( x + 4 y ) ^ { 2 } - 9 a ^ { 2 }(x+4y)2−9a2 completely.

Find the greatest common factor of the expressions 15ab215 a b ^ { 2 }15ab2 and 45a2b345 a ^ { 2 } b ^ { 3 }45a2b3 .

Use the Zero-Factor Property to solve the equation below. 28(a+5)(a−7)=028 ( a + 5 ) ( a - 7 ) = 028(a+5)(a−7)=0

Fundamentals of Algebra

Linear Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions, Equations, and Functions

Radicals and Complex Numbers

Quadratic Equations, Functions, and Inequalities

Exponential and Logarithmic Functions

Conics

Sequences, Series, and the Binomial Theorem

Filters

Find the sum $\left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right) + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right)$ .

Solve the equation below by factoring. $x ^ { 4 } - 2 x ^ { 3 } - 16 x ^ { 2 } + 32 x = 0$

Find two real numbers b such that the expression $x ^ { 2 } + b x + 196$ is a perfect square trinomial.

Subtract $3 y ^ { 2 } - 3 y ^ { 3 } \text { from } 9 y ^ { 5 } + 9 y ^ { 3 }$ .

Find $h ( x ) = f ( x ) + g ( x )$ where $f ( x ) = 8 x ^ { 3 } - 9 x ^ { 2 } + 8$ and $g ( x ) = 10 - x - x ^ { 2 } - 9 x ^ { 3 }$

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+5 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box if dimensions increase by 6 inches.

Find the sum $( 6 x + 2 ) + ( 8 x - 6 )$ .

Factor the trinomial $t ^ { 2 } - 6 t - 7$ .

Find the greatest common factor of the expressions $7 ( x - 4 ) ^ { 2 }$ and $7 ( x - 4 ) ^ { 3 }$ .

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n } y ^ { 3 xn - 1 } } { x ^ { n } y ^ { n - 4 } }$

Multiply: $- 9 u \left( - 5 u ^ { 2 } + 2 \right)$

Factor the expression by factoring out the common binomial factor. $( 2 x - 3 ) ( x + 5 ) + ( 7 x + 1 ) ( x + 5 )$

Use a graphing calculator to find any x -intercepts of the graph $y = 7 x ^ { 3 } - 95 x ^ { 2 } - 42 x$ .

Factor the expression $( x + 4 y ) ^ { 2 } - 9 a ^ { 2 }$ completely.

Find the greatest common factor of the expressions $15 a b ^ { 2 }$ and $45 a ^ { 2 } b ^ { 3 }$ .

Use the Zero-Factor Property to solve the equation below. $28 ( a + 5 ) ( a - 7 ) = 0$