Question 1

Factor completely.
-$$x ^ { 2 } + 12 x + 36 - x ^ { 4 }$$

Accepted Answer

A)  $\left( x + 6 - x ^ { 2 } \right) ^ { 2 }$ 
B)  $\left( x - 6 + x ^ { 2 } \right) \left( x - 6 - x ^ { 2 } \right)$ 
C)  $\left( x + 6 + x ^ { 2 } \right) \left( x + 6 - x ^ { 2 } \right)$ 
D)  prime polynomial 
A)  $\left( x + 6 - x ^ { 2 } \right) ^ { 2 }$ 
B)  $\left( x - 6 + x ^ { 2 } \right) \left( x - 6 - x ^ { 2 } \right)$ 
C)  $\left( x + 6 + x ^ { 2 } \right) \left( x + 6 - x ^ { 2 } \right)$ 
D)  prime polynomial

Question 2

Factor the trinomial.
-$5 x ^ { 2 } + 3 x - 2$

Accepted Answer

A)  $( 5 x + 1 ) ( x - 2 )$ 
B)  $( 5 x + 2 ) ( x - 1 )$ 
C)  $( 5 x - 2 ) ( x + 1 )$ 
D)  $( 5 x - 1 ) ( x + 2 )$ 
A)  $( 5 x + 1 ) ( x - 2 )$ 
B)  $( 5 x + 2 ) ( x - 1 )$ 
C)  $( 5 x - 2 ) ( x + 1 )$ 
D)  $( 5 x - 1 ) ( x + 2 )$

Question 3

Factor the polynomial completely.
-$x ^ { 2 } + 2 x y - 48 y ^ { 2 }$

Accepted Answer

A)  $( x - 8 y ) ( x + y )$ 
B)  $( x + 8 y ) ( x - 6 y )$ 
C)  $( x - 8 y ) ( x - 6 y )$ 
D)  prime polynomial 
A)  $( x - 8 y ) ( x + y )$ 
B)  $( x + 8 y ) ( x - 6 y )$ 
C)  $( x - 8 y ) ( x - 6 y )$ 
D)  prime polynomial

Question 4

Multiply.
-$$( x + 12 y ) ( x - 12 y )$$

Accepted Answer

A)  $x ^ { 2 } - 24 x y - 144 y ^ { 2 }$ 
B)  $x ^ { 2 } - 144 y ^ { 2 }$ 
C)  $x ^ { 2 } - 24 y ^ { 2 }$ 
D)  $x ^ { 2 } + 24 x y - 144 y ^ { 2 }$ 
A)  $x ^ { 2 } - 24 x y - 144 y ^ { 2 }$ 
B)  $x ^ { 2 } - 144 y ^ { 2 }$ 
C)  $x ^ { 2 } - 24 y ^ { 2 }$ 
D)  $x ^ { 2 } + 24 x y - 144 y ^ { 2 }$

Question 5

Use substitution to factor the polynomial completely.
-$4 x ^ { 4 } + 4 x ^ { 2 } - 15$

Accepted Answer

A)  $\left( 2 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } + 5 \right)$ 
B)  $\left( 4 x ^ { 2 } - 3 \right) \left( x ^ { 2 } + 5 \right)$ 
C)  $\left( 2 x ^ { 2 } - 15 \right) \left( 2 x ^ { 2 } + 1 \right)$ 
D)  $\left( 2 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } - 5 \right)$ 
A)  $\left( 2 x ^ { 2 } - 3 \right) \left( 2 x ^ { 2 } + 5 \right)$ 
B)  $\left( 4 x ^ { 2 } - 3 \right) \left( x ^ { 2 } + 5 \right)$ 
C)  $\left( 2 x ^ { 2 } - 15 \right) \left( 2 x ^ { 2 } + 1 \right)$ 
D)  $\left( 2 x ^ { 2 } + 3 \right) \left( 2 x ^ { 2 } - 5 \right)$

Question 6

Divide.
-$x ^ { 2 } + 7 x + 5$ by $x + 4$

Accepted Answer

A)  $x + 3 + \frac { 7 } { x + 4 }$ 
B)  $\frac { x + 3 } { x + 4 }$ 
C)  $x + 4$ 
D)  $x + 3 - \frac { 7 } { x + 4 }$ 
A)  $x + 3 + \frac { 7 } { x + 4 }$ 
B)  $\frac { x + 3 } { x + 4 }$ 
C)  $x + 4$ 
D)  $x + 3 - \frac { 7 } { x + 4 }$

Question 7

Solve.
-The polynomial function $\mathrm { P } ( x ) = 0.95 x - 84$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes, $\mathrm { P } ( \mathrm { x } )$. Find $\mathrm { P } ( 800 )$, the profit the vendor makes from selling 800 pretzels.

Accepted Answer

A)  $- \$ 74.50$ 
B)  $\$ 716$ 
C)  $\$ 676$ 
D)  $\$ 760$ 
A)  $- \$ 74.50$ 
B)  $\$ 716$ 
C)  $\$ 676$ 
D)  $\$ 760$

Question 8

Factor out the greatest common factor.
-$12 x - 6$

Accepted Answer

A)  $6 ( 2 x - 1 )$ 
B)  $6 ( x - 1 )$ 
C)  $6 x ( 2 x - 1 )$ 
D)  $6 ( x - 2 )$ 
A)  $6 ( 2 x - 1 )$ 
B)  $6 ( x - 1 )$ 
C)  $6 x ( 2 x - 1 )$ 
D)  $6 ( x - 2 )$

Question 9

Find all positive and negative integers b such that the trinomial is factorable.
-$$7 x ^ { 2 } + b x - 1$$

Accepted Answer

A)  6 
B)  $\pm 6$ 
C)  8 
D)  $\pm 8$ 
A)  6 
B)  $\pm 6$ 
C)  8 
D)  $\pm 8$

Question 10

For the given f(x $$f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$$
-$$f ( x ) = - 3 x ^ { 3 } - 18 x ^ { 2 } - 20 x + 16 ; g ( x ) = x + 4$$

Accepted Answer

A)  $3 x ^ { 2 } + 4 x - 4 ; x \neq 4$ 
B)  $- 3 x ^ { 2 } - 6 x + 4 ; x \neq - 4$ 
C)  $3 x ^ { 2 } - 4 x + 4 ; x \neq - 4$ 
D)  $- 3 x ^ { 2 } - 6 x + 4 ; x \neq 4$ 
A)  $3 x ^ { 2 } + 4 x - 4 ; x \neq 4$ 
B)  $- 3 x ^ { 2 } - 6 x + 4 ; x \neq - 4$ 
C)  $3 x ^ { 2 } - 4 x + 4 ; x \neq - 4$ 
D)  $- 3 x ^ { 2 } - 6 x + 4 ; x \neq 4$

Question 11

Subtract.
-Subtract $( x + 5 )$ from $( 8 x + 7 )$

Accepted Answer

A)  $8 x + 12$ 
B)  $7 x + 12$ 
C)  $8 x + 2$ 
D)  $7 x + 2$ 
A)  $8 x + 12$ 
B)  $7 x + 12$ 
C)  $8 x + 2$ 
D)  $7 x + 2$

Question 12

Find the function value.
-If $Q ( x ) = 3 x ^ { 2 } - 5 x - 3$, find $Q ( 0 )$

Accepted Answer

A)  $- 5$ 
B)  3 
C)  0 
D)  $- 3$ 
A)  $- 5$ 
B)  3 
C)  0 
D)  $- 3$

Question 13

Perform the indicated operation.
-$( 5 x + 3 ) ( 5 x + 12 )$

Accepted Answer

A)  $25 x ^ { 2 } + 75 x + 36$ 
B)  $10 x ^ { 2 } + 75 x + 36$ 
C)  $10 x ^ { 2 } + 75 x + 75$ 
D)  $25 x ^ { 2 } + 75 x + 75$ 
A)  $25 x ^ { 2 } + 75 x + 36$ 
B)  $10 x ^ { 2 } + 75 x + 36$ 
C)  $10 x ^ { 2 } + 75 x + 75$ 
D)  $25 x ^ { 2 } + 75 x + 75$

Question 14

Factor.
-$$x ^ { 2 } - 8 x y + 16 y ^ { 2 }$$

Accepted Answer

A)  $( x - 4 y ) ^ { 2 }$ 
B)  $( x - 4 y ) ( x + 4 y )$ 
C)  $( x + 4 y ) ^ { 2 }$ 
D)  prime polynomial 
A)  $( x - 4 y ) ^ { 2 }$ 
B)  $( x - 4 y ) ( x + 4 y )$ 
C)  $( x + 4 y ) ^ { 2 }$ 
D)  prime polynomial

Question 15

Divide.
-$$\left( 25 x ^ { 3 } - 10 x ^ { 2 } - 23 x + 14 \right) \div ( - 5 x - 2 )$$

Accepted Answer

A)  $- 5 x ^ { 2 } + 4 x + 3 + \frac { 20 } { - 5 x - 2 }$ 
B)  $- 5 x ^ { 2 } + 4 x + 3 + \frac { 23 } { - 5 x - 2 }$ 
C)  $- 5 x ^ { 2 } + 4 x + 3$ 
D)  $x ^ { 2 } + 3 + \frac { 23 } { - 5 x - 2 }$ 
A)  $- 5 x ^ { 2 } + 4 x + 3 + \frac { 20 } { - 5 x - 2 }$ 
B)  $- 5 x ^ { 2 } + 4 x + 3 + \frac { 23 } { - 5 x - 2 }$ 
C)  $- 5 x ^ { 2 } + 4 x + 3$ 
D)  $x ^ { 2 } + 3 + \frac { 23 } { - 5 x - 2 }$

Question 16

Evaluate the polynomial function.
-If $f ( x ) = x ^ { 2 } - 5 x + 7$, find $f ( a + h )$.

Accepted Answer

A)  $a ^ { 2 } + h ^ { 2 } - 5 a - 5 h + 14$ 
B)  $a ^ { 2 } + h ^ { 2 } - 5 a - 5 h + 7$ 
C)  $a ^ { 2 } + 2 a h + h ^ { 2 } - 5 a - 5 h + 7$ 
D)  $a ^ { 2 } + a h + h ^ { 2 } - 5 a - 5 h - 5$ 
A)  $a ^ { 2 } + h ^ { 2 } - 5 a - 5 h + 14$ 
B)  $a ^ { 2 } + h ^ { 2 } - 5 a - 5 h + 7$ 
C)  $a ^ { 2 } + 2 a h + h ^ { 2 } - 5 a - 5 h + 7$ 
D)  $a ^ { 2 } + a h + h ^ { 2 } - 5 a - 5 h - 5$

Question 17

Find the function.
-If $P ( x ) = 8 x$ and $Q ( x ) = - 11 x - 12$, find $P ( x ) \cdot Q ( x )$

Accepted Answer

A)  $- 11 x ^ { 2 } - 96 x$ 
B)  $- 88 x ^ { 2 } + 8 x$ 
C)  $- 88 x ^ { 2 }$ 
D)  $- 88 x ^ { 2 } - 96 x$ 
A)  $- 11 x ^ { 2 } - 96 x$ 
B)  $- 88 x ^ { 2 } + 8 x$ 
C)  $- 88 x ^ { 2 }$ 
D)  $- 88 x ^ { 2 } - 96 x$

Question 18

Solve the equation.
-$$( x - 3 ) ( x + 8 ) = 0$$

Accepted Answer

A)  $\{ - 3,8 \}$ 
B)  $\{ 3 , - 8,0 \}$ 
C)  $\{ 3,8 \}$ 
D)  $\{ 3 , - 8 \}$ 
A)  $\{ - 3,8 \}$ 
B)  $\{ 3 , - 8,0 \}$ 
C)  $\{ 3,8 \}$ 
D)  $\{ 3 , - 8 \}$

Question 19

Factor.
-$$( x - 7 ) ^ { 2 } - y ^ { 2 }$$

Accepted Answer

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

Question 20

Solve.
-An open-topped box has a square base and a height of 15 inches. If each of the bottom edges of the box has lengt inches, find the amount of material needed to construct the box. Write the answer in factored form.

Accepted Answer

A)  $x ( x + 30 ) s q$ in. 
B)  $\left( x ^ { 2 } + 60 \right) s q$ in. 
C)  $x ( x + 60 )$ sq in. 
D)  $x ( x + 15 ) s q$ in. 
A)  $x ( x + 30 ) s q$ in. 
B)  $\left( x ^ { 2 } + 60 \right) s q$ in. 
C)  $x ( x + 60 )$ sq in. 
D)  $x ( x + 15 ) s q$ in.

Factor completely. - $x ^ { 2 } + 12 x + 36 - x ^ { 4 }$

Factor the trinomial. - $5 x ^ { 2 } + 3 x - 2$

Factor the polynomial completely. - $x ^ { 2 } + 2 x y - 48 y ^ { 2 }$

Multiply. - $( x + 12 y ) ( x - 12 y )$

Use substitution to factor the polynomial completely. - $4 x ^ { 4 } + 4 x ^ { 2 } - 15$

Divide. - $x ^ { 2 } + 7 x + 5$ by $x + 4$

Factor out the greatest common factor. - $12 x - 6$

Find all positive and negative integers b such that the trinomial is factorable. - $7 x ^ { 2 } + b x - 1$

For the given f(x $f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$ - $f ( x ) = - 3 x ^ { 3 } - 18 x ^ { 2 } - 20 x + 16 ; g ( x ) = x + 4$

Subtract. -Subtract $( x + 5 )$ from $( 8 x + 7 )$

Find the function value. -If $Q ( x ) = 3 x ^ { 2 } - 5 x - 3$ , find $Q ( 0 )$

Perform the indicated operation. - $( 5 x + 3 ) ( 5 x + 12 )$

Factor. - $x ^ { 2 } - 8 x y + 16 y ^ { 2 }$

Divide. - $\left( 25 x ^ { 3 } - 10 x ^ { 2 } - 23 x + 14 \right) \div ( - 5 x - 2 )$

Evaluate the polynomial function. -If $f ( x ) = x ^ { 2 } - 5 x + 7$ , find $f ( a + h )$ .

Find the function. -If $P ( x ) = 8 x$ and $Q ( x ) = - 11 x - 12$ , find $P ( x ) \cdot Q ( x )$

Solve the equation. - $( x - 3 ) ( x + 8 ) = 0$

Factor. - $( x - 7 ) ^ { 2 } - y ^ { 2 }$

Solve. -An open-topped box has a square base and a height of 15 inches. If each of the bottom edges of the box has lengt inches, find the amount of material needed to construct the box. Write the answer in factored form.

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

Graphs and Functions

Systems of Equations and Inequalities

Rational Expressions

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Fractions

Filters

Exam 5: Polynomials and Polynomial Functions

Factor completely. - x2+12x+36−x4x ^ { 2 } + 12 x + 36 - x ^ { 4 }x2+12x+36−x4

Factor the trinomial. - 5x2+3x−25 x ^ { 2 } + 3 x - 25x2+3x−2

Factor the polynomial completely. - x2+2xy−48y2x ^ { 2 } + 2 x y - 48 y ^ { 2 }x2+2xy−48y2

Multiply. - (x+12y)(x−12y)( x + 12 y ) ( x - 12 y )(x+12y)(x−12y)

Use substitution to factor the polynomial completely. - 4x4+4x2−154 x ^ { 4 } + 4 x ^ { 2 } - 154x4+4x2−15

Divide. - x2+7x+5x ^ { 2 } + 7 x + 5x2+7x+5 by x+4x + 4x+4

Factor out the greatest common factor. - 12x−612 x - 612x−6

Find all positive and negative integers b such that the trinomial is factorable. - 7x2+bx−17 x ^ { 2 } + b x - 17x2+bx−1

Subtract. -Subtract (x+5)( x + 5 )(x+5) from (8x+7)( 8 x + 7 )(8x+7)

Find the function value. -If Q(x)=3x2−5x−3Q ( x ) = 3 x ^ { 2 } - 5 x - 3Q(x)=3x2−5x−3 , find Q(0)Q ( 0 )Q(0)

Perform the indicated operation. - (5x+3)(5x+12)( 5 x + 3 ) ( 5 x + 12 )(5x+3)(5x+12)

Factor. - x2−8xy+16y2x ^ { 2 } - 8 x y + 16 y ^ { 2 }x2−8xy+16y2

Divide. - (25x3−10x2−23x+14)÷(−5x−2)\left( 25 x ^ { 3 } - 10 x ^ { 2 } - 23 x + 14 \right) \div ( - 5 x - 2 )(25x3−10x2−23x+14)÷(−5x−2)

Evaluate the polynomial function. -If f(x)=x2−5x+7f ( x ) = x ^ { 2 } - 5 x + 7f(x)=x2−5x+7 , find f(a+h)f ( a + h )f(a+h) .

Find the function. -If P(x)=8xP ( x ) = 8 xP(x)=8x and Q(x)=−11x−12Q ( x ) = - 11 x - 12Q(x)=−11x−12 , find P(x)⋅Q(x)P ( x ) \cdot Q ( x )P(x)⋅Q(x)

Solve the equation. - (x−3)(x+8)=0( x - 3 ) ( x + 8 ) = 0(x−3)(x+8)=0

Factor. - (x−7)2−y2( x - 7 ) ^ { 2 } - y ^ { 2 }(x−7)2−y2