Question 1

Multiply.
-$$( x + 1 ) ( x - 1 ) ( 4 x + 3 )$$

Accepted Answer

A)  $4 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 3$ 
B)  $4 x ^ { 3 } + 3 x ^ { 2 } + 4 x + 3$ 
C)  $4 x ^ { 3 } - 5 x ^ { 2 } - 2 x + 3$ 
D)  $4 x ^ { 3 } + 11 x ^ { 2 } + 10 x + 3$ 
A)  $4 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 3$ 
B)  $4 x ^ { 3 } + 3 x ^ { 2 } + 4 x + 3$ 
C)  $4 x ^ { 3 } - 5 x ^ { 2 } - 2 x + 3$ 
D)  $4 x ^ { 3 } + 11 x ^ { 2 } + 10 x + 3$

Question 2

Solve the equation for the variable.
-$$n ( 4 n + 6 ) = 4$$

Accepted Answer

A)  $\left\{ 0 , \frac { 3 } { 2 } \right\}$ 
B)  $\{ 4,2 \}$ 
C)  $\left\{ 0 , - \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } , - 2 \right\}$ 
A)  $\left\{ 0 , \frac { 3 } { 2 } \right\}$ 
B)  $\{ 4,2 \}$ 
C)  $\left\{ 0 , - \frac { 3 } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } , - 2 \right\}$

Question 3

Factor.
-$$( x + 8 ) ^ { 2 } - 9$$

Accepted Answer

A)  $( x - 5 ) ( x - 11 )$ 
B)  $( x + 17 ) ( x - 1 )$ 
C)  $x ^ { 2 } + 16 x + 55$ 
D)  $( x + 11 ) ( x + 5 )$ 
A)  $( x - 5 ) ( x - 11 )$ 
B)  $( x + 17 ) ( x - 1 )$ 
C)  $x ^ { 2 } + 16 x + 55$ 
D)  $( x + 11 ) ( x + 5 )$

Question 4

Multiply.
-$$\left( 2 x ^ { 3 } - 7 \right) \left( x ^ { 2 } - 11 \right)$$

Accepted Answer

A)  $2 x ^ { 5 } - 22 x ^ { 3 } - 7 x ^ { 2 } - 77$ 
B)  $2 x ^ { 5 } - 22 x ^ { 3 } - 7 x ^ { 2 } + 77$ 
C)  $3 x ^ { 5 } - 13 x ^ { 3 } - 8 x ^ { 2 } + 18$ 
D)  $2 x ^ { 5 } - 29 x ^ { 3 } + 77$ 
A)  $2 x ^ { 5 } - 22 x ^ { 3 } - 7 x ^ { 2 } - 77$ 
B)  $2 x ^ { 5 } - 22 x ^ { 3 } - 7 x ^ { 2 } + 77$ 
C)  $3 x ^ { 5 } - 13 x ^ { 3 } - 8 x ^ { 2 } + 18$ 
D)  $2 x ^ { 5 } - 29 x ^ { 3 } + 77$

Question 5

Solve.
-A projectile is fired upward from the ground with an initial velocity of 200 feet per second. Neglecting air resistance, the height of the projectile at any time $t$ can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } +$ $200 \mathrm { t }$. Find the height of the projectile at $\mathrm { t } = 4$ seconds.

Accepted Answer

A)  $644 \mathrm { ft }$ 
B)  $544 \mathrm { ft }$ 
C)  $736 \mathrm { ft }$ 
D)  $800 \mathrm { ft }$ 
A)  $644 \mathrm { ft }$ 
B)  $544 \mathrm { ft }$ 
C)  $736 \mathrm { ft }$ 
D)  $800 \mathrm { ft }$

Question 6

Factor the polynomial.
-$$x ^ { 3 } - 11 x y ^ { 4 } + 11 x ^ { 3 } y ^ { 6 } - 19 x ^ { 3 } y ^ { 4 }$$

Accepted Answer

A)  $x \left( x ^ { 2 } - 11 y ^ { 4 } + 11 x ^ { 2 } y ^ { 6 } - 19 x ^ { 2 } y ^ { 4 } \right)$ 
B)  $x y ^ { 4 } \left( x ^ { 2 } - 11 + 11 x ^ { 2 } y ^ { 2 } - 19 x ^ { 2 } \right)$ 
C)  $x y \left( x ^ { 2 } - 11 y ^ { 3 } + 11 x ^ { 2 } y ^ { 5 } - 19 x ^ { 2 } y ^ { 3 } \right)$ 
D)  $x ^ { 2 } \left( x ^ { 2 } - 11 y ^ { 3 } + 11 x ^ { 2 } y ^ { 5 } - 19 x ^ { 2 } y ^ { 3 } \right)$ 
A)  $x \left( x ^ { 2 } - 11 y ^ { 4 } + 11 x ^ { 2 } y ^ { 6 } - 19 x ^ { 2 } y ^ { 4 } \right)$ 
B)  $x y ^ { 4 } \left( x ^ { 2 } - 11 + 11 x ^ { 2 } y ^ { 2 } - 19 x ^ { 2 } \right)$ 
C)  $x y \left( x ^ { 2 } - 11 y ^ { 3 } + 11 x ^ { 2 } y ^ { 5 } - 19 x ^ { 2 } y ^ { 3 } \right)$ 
D)  $x ^ { 2 } \left( x ^ { 2 } - 11 y ^ { 3 } + 11 x ^ { 2 } y ^ { 5 } - 19 x ^ { 2 } y ^ { 3 } \right)$

Question 7

Find the value of c that makes the trinomial a perfect square trinomial.
-$$x ^ { 2 } - 12 x + c$$

Accepted Answer

A)  36 or $- 36$ 
B)  $- 36$ 
C)  36 
D)  No solution 
A)  36 or $- 36$ 
B)  $- 36$ 
C)  36 
D)  No solution

Question 8

Find the function value.
-If $P ( x ) = 5 x ^ { 2 } - 9 x$, find $P ( - 2 )$.

Accepted Answer

A)  8 
B)  20 
C)  9 
D)  38 
A)  8 
B)  20 
C)  9 
D)  38

Question 9

Factor the polynomial.
-$$x ^ { 2 } - 8 x - 33$$

Accepted Answer

A)  $( x + 11 ) ( x - 3 )$ 
B)  $( x - 11 ) ( x + 3 )$ 
C)  $( x - 33 ) ( x + 1 )$ 
D)  prime polynomial 
A)  $( x + 11 ) ( x - 3 )$ 
B)  $( x - 11 ) ( x + 3 )$ 
C)  $( x - 33 ) ( x + 1 )$ 
D)  prime polynomial

Question 10

Factor completely.
-$75 x ^ { 2 } y - 108 y$

Accepted Answer

A)  $3 y ( 5 x - 6 ) ^ { 2 }$ 
B)  $3 y ( 5 x + 6 ) ( 5 x - 6 )$ 
C)  $3 y ( 5 x + 6 ) ^ { 2 }$ 
D)  prime polynomial 
A)  $3 y ( 5 x - 6 ) ^ { 2 }$ 
B)  $3 y ( 5 x + 6 ) ( 5 x - 6 )$ 
C)  $3 y ( 5 x + 6 ) ^ { 2 }$ 
D)  prime polynomial

Question 11

Solve the equation.
-$$( 6 x + 1 ) ( 5 x - 3 ) = 0$$

Accepted Answer

A)  $\{ 5,2 \}$ 
B)  $\left\{ - \frac { 1 } { 6 } , \frac { 3 } { 5 } \right\}$ 
C)  $\left\{ \frac { 1 } { 6 } , - \frac { 3 } { 5 } \right\}$ 
D)  $\left\{ 6 , \frac { 5 } { 3 } \right\}$ 
A)  $\{ 5,2 \}$ 
B)  $\left\{ - \frac { 1 } { 6 } , \frac { 3 } { 5 } \right\}$ 
C)  $\left\{ \frac { 1 } { 6 } , - \frac { 3 } { 5 } \right\}$ 
D)  $\left\{ 6 , \frac { 5 } { 3 } \right\}$

Question 12

Solve the equation for the variable.
-$$( x + 1 ) ( x - 1 ) = 3 ( x + 3 )$$

Accepted Answer

A)  $\{ - 5,2 \}$ 
B)  $\{ 2,5 \}$ 
C)  $\{ - 5 , - 2 \}$ 
D)  $\{ - 2,5 \}$ 
A)  $\{ - 5,2 \}$ 
B)  $\{ 2,5 \}$ 
C)  $\{ - 5 , - 2 \}$ 
D)  $\{ - 2,5 \}$

Question 13

Solve.
-At the end of t years, the amount of money A in a savings account earning simple interest from an initial investment of $\mathrm { P }$ dollars at monthly rate $\mathrm { r }$ is given by the formula $\mathrm { A } = \mathrm { P } + 12 \mathrm { Prt }$. Write an equivalent equation by factoring the expression $\mathrm { P } + 12$ Prt.

Accepted Answer

A)  $\mathrm { A } = \mathrm { P } ( 12 +$ Prt $)$ 
B)  $\mathrm { A } = \mathrm { P } ( 12 + \mathrm { rt } )$ 
C)  $A = P ( P + 12 r t )$ 
D)  $\mathrm { A } = \mathrm { P } ( 1 + 12 \mathrm { rt } )$ 
A)  $\mathrm { A } = \mathrm { P } ( 12 +$ Prt $)$ 
B)  $\mathrm { A } = \mathrm { P } ( 12 + \mathrm { rt } )$ 
C)  $A = P ( P + 12 r t )$ 
D)  $\mathrm { A } = \mathrm { P } ( 1 + 12 \mathrm { rt } )$

Question 14

Factor the polynomial completely.
-$3 x ^ { 2 } - 18 x + 24$

Accepted Answer

A)  $3 ( x - 8 ) ( x + 1 )$ 
B)  $3 ( x - 2 ) ( x - 4 )$ 
C)  $( x - 2 ) ( 3 x - 12 )$ 
D)  prime polynomial 
A)  $3 ( x - 8 ) ( x + 1 )$ 
B)  $3 ( x - 2 ) ( x - 4 )$ 
C)  $( x - 2 ) ( 3 x - 12 )$ 
D)  prime polynomial

Question 15

Solve.
-A object is thrown upward with an initial velocity of 21 feet per second from the top of a 572 -foot building. The height of the object above the ground at any time $t$ can be described by the polynomial function $P ( t ) = - 16 t ^ { 2 } + 21 t + 572$. Find the height of the object at $t = 4$ seconds.

Accepted Answer

A)  $400 \mathrm { ft }$ 
B)  $592 \mathrm { ft }$ 
C)  $572 \mathrm { ft }$ 
D)  $337 \mathrm { ft }$ 
A)  $400 \mathrm { ft }$ 
B)  $592 \mathrm { ft }$ 
C)  $572 \mathrm { ft }$ 
D)  $337 \mathrm { ft }$

Question 16

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of
these.
-$$9 x ^ { 3 } + 16 x ^ { 4 } + 9 x ^ { 2 } + 9$$

Accepted Answer

A)  trinomial of degree 4 
B)  degree 4 ; none of these 
C)  degree 3 ; none of these 
D)  trinomial of degree 3 
A)  trinomial of degree 4 
B)  degree 4 ; none of these 
C)  degree 3 ; none of these 
D)  trinomial of degree 3

Question 17

Factor the polynomial completely.
-$20 x ^ { 2 } - 23 x y + 6 y ^ { 2 }$

Accepted Answer

A)  $( 20 x + 3 y ) ( x + 2 y )$ 
B)  $( 4 x + 3 y ) ( 5 x + 2 y )$ 
C)  $( 4 x - 3 y ) ( 5 x - 2 y )$ 
D)  prime polynomial 
A)  $( 20 x + 3 y ) ( x + 2 y )$ 
B)  $( 4 x + 3 y ) ( 5 x + 2 y )$ 
C)  $( 4 x - 3 y ) ( 5 x - 2 y )$ 
D)  prime polynomial

Question 18

Divide.
-$- 16 x ^ { 10 } - 28 x ^ { 7 }$ by $- 4 x ^ { 4 }$

Accepted Answer

A)  $4 x ^ { 6 } + 7 x ^ { 3 }$ 
B)  $- 16 x ^ { 10 } + 7 x ^ { 3 }$ 
C)  $4 x ^ { 6 } - 28 x ^ { 7 }$ 
D)  $11  x ^ {13 }$ 
A)  $4 x ^ { 6 } + 7 x ^ { 3 }$ 
B)  $- 16 x ^ { 10 } + 7 x ^ { 3 }$ 
C)  $4 x ^ { 6 } - 28 x ^ { 7 }$ 
D)  $11  x ^ {13 }$

Question 19

Perform the indicated operation.
-Use synthetic division to divide $- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20$ by $x + 4$

Accepted Answer

A)  $- \frac { 1 } { 2 } x ^ { 2 } - \frac { 5 } { 2 } x - \frac { 3 } { 4 }$ 
B)  $- 2 x ^ { 2 } - 2 x + 5$ 
C)  $- 2 x - 2$ 
D)  $2 x ^ { 2 } - 4 x + 5$ 
A)  $- \frac { 1 } { 2 } x ^ { 2 } - \frac { 5 } { 2 } x - \frac { 3 } { 4 }$ 
B)  $- 2 x ^ { 2 } - 2 x + 5$ 
C)  $- 2 x - 2$ 
D)  $2 x ^ { 2 } - 4 x + 5$

Question 20

Find the function.
-If $P ( x ) = 2 x + 5$ and $Q ( x ) = - 3 x ^ { 2 } + 7 x + 5$, find $P ( x ) + Q ( x )$

Accepted Answer

A)  $- 3 x ^ { 2 } + 9 x - 10$ 
B)  $- 3 x ^ { 2 } + 9 x + 10$ 
C)  $- 3 x ^ { 2 } - 9 x + 10$ 
D)  $3 x ^ { 2 } + 9 x + 10$ 
A)  $- 3 x ^ { 2 } + 9 x - 10$ 
B)  $- 3 x ^ { 2 } + 9 x + 10$ 
C)  $- 3 x ^ { 2 } - 9 x + 10$ 
D)  $3 x ^ { 2 } + 9 x + 10$

Multiply. - $( x + 1 ) ( x - 1 ) ( 4 x + 3 )$

Solve the equation for the variable. - $n ( 4 n + 6 ) = 4$

Factor. - $( x + 8 ) ^ { 2 } - 9$

Multiply. - $\left( 2 x ^ { 3 } - 7 \right) \left( x ^ { 2 } - 11 \right)$

Factor the polynomial. - $x ^ { 3 } - 11 x y ^ { 4 } + 11 x ^ { 3 } y ^ { 6 } - 19 x ^ { 3 } y ^ { 4 }$

Find the value of c that makes the trinomial a perfect square trinomial. - $x ^ { 2 } - 12 x + c$

Find the function value. -If $P ( x ) = 5 x ^ { 2 } - 9 x$ , find $P ( - 2 )$ .

Factor the polynomial. - $x ^ { 2 } - 8 x - 33$

Factor completely. - $75 x ^ { 2 } y - 108 y$

Solve the equation. - $( 6 x + 1 ) ( 5 x - 3 ) = 0$

Solve the equation for the variable. - $( x + 1 ) ( x - 1 ) = 3 ( x + 3 )$

Factor the polynomial completely. - $3 x ^ { 2 } - 18 x + 24$

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - $9 x ^ { 3 } + 16 x ^ { 4 } + 9 x ^ { 2 } + 9$

Factor the polynomial completely. - $20 x ^ { 2 } - 23 x y + 6 y ^ { 2 }$

Divide. - $- 16 x ^ { 10 } - 28 x ^ { 7 }$ by $- 4 x ^ { 4 }$

Perform the indicated operation. -Use synthetic division to divide $- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20$ by $x + 4$

Find the function. -If $P ( x ) = 2 x + 5$ and $Q ( x ) = - 3 x ^ { 2 } + 7 x + 5$ , find $P ( x ) + Q ( x )$

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

Multiply. - (x+1)(x−1)(4x+3)( x + 1 ) ( x - 1 ) ( 4 x + 3 )(x+1)(x−1)(4x+3)

Solve the equation for the variable. - n(4n+6)=4n ( 4 n + 6 ) = 4n(4n+6)=4

Factor. - (x+8)2−9( x + 8 ) ^ { 2 } - 9(x+8)2−9

Multiply. - (2x3−7)(x2−11)\left( 2 x ^ { 3 } - 7 \right) \left( x ^ { 2 } - 11 \right)(2x3−7)(x2−11)

Factor the polynomial. - x3−11xy4+11x3y6−19x3y4x ^ { 3 } - 11 x y ^ { 4 } + 11 x ^ { 3 } y ^ { 6 } - 19 x ^ { 3 } y ^ { 4 }x3−11xy4+11x3y6−19x3y4

Find the value of c that makes the trinomial a perfect square trinomial. - x2−12x+cx ^ { 2 } - 12 x + cx2−12x+c

Find the function value. -If P(x)=5x2−9xP ( x ) = 5 x ^ { 2 } - 9 xP(x)=5x2−9x , find P(−2)P ( - 2 )P(−2) .

Factor the polynomial. - x2−8x−33x ^ { 2 } - 8 x - 33x2−8x−33

Factor completely. - 75x2y−108y75 x ^ { 2 } y - 108 y75x2y−108y

Solve the equation. - (6x+1)(5x−3)=0( 6 x + 1 ) ( 5 x - 3 ) = 0(6x+1)(5x−3)=0

Solve the equation for the variable. - (x+1)(x−1)=3(x+3)( x + 1 ) ( x - 1 ) = 3 ( x + 3 )(x+1)(x−1)=3(x+3)

Factor the polynomial completely. - 3x2−18x+243 x ^ { 2 } - 18 x + 243x2−18x+24

Find the degree of the polynomial and indicate whether the polynomial is a monomial, binomial, trinomial, or none of these. - 9x3+16x4+9x2+99 x ^ { 3 } + 16 x ^ { 4 } + 9 x ^ { 2 } + 99x3+16x4+9x2+9

Factor the polynomial completely. - 20x2−23xy+6y220 x ^ { 2 } - 23 x y + 6 y ^ { 2 }20x2−23xy+6y2

Divide. - −16x10−28x7- 16 x ^ { 10 } - 28 x ^ { 7 }−16x10−28x7 by −4x4- 4 x ^ { 4 }−4x4

Perform the indicated operation. -Use synthetic division to divide −2x3−10x2−3x+20- 2 x ^ { 3 } - 10 x ^ { 2 } - 3 x + 20−2x3−10x2−3x+20 by x+4x + 4x+4

Find the function. -If P(x)=2x+5P ( x ) = 2 x + 5P(x)=2x+5 and Q(x)=−3x2+7x+5Q ( x ) = - 3 x ^ { 2 } + 7 x + 5Q(x)=−3x2+7x+5 , find P(x)+Q(x)P ( x ) + Q ( x )P(x)+Q(x)