Question 1

Multiply.
-$$( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)$$

Accepted Answer

A)  $x ^ { 4 } + 10 x ^ { 3 } - 250 x - 625$ 
B)  $x ^ { 4 } - 625$ 
C)  $x ^ { 4 } + 50 x ^ { 2 } + 625$ 
D)  $x ^ { 4 } + 10 x ^ { 3 } + 50 x ^ { 2 } - 250 x - 625$ 
A)  $x ^ { 4 } + 10 x ^ { 3 } - 250 x - 625$ 
B)  $x ^ { 4 } - 625$ 
C)  $x ^ { 4 } + 50 x ^ { 2 } + 625$ 
D)  $x ^ { 4 } + 10 x ^ { 3 } + 50 x ^ { 2 } - 250 x - 625$

Question 2

Divide.
-$$\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 13 x - 9 } { x - \frac { 1 } { 2 } }$$

Accepted Answer

A)  $4 x ^ { 2 } - 10 x + 18$ 
B)  $4 x ^ { 2 } + 10 x + 18$ 
C)  $4 x ^ { 2 } + 6 x + 10 + \frac { 18 } { x - \frac { 1 } { 2 } }$ 
D)  $4 x ^ { 2 } + 10 x + 18 - \frac { 18 } { x - \frac { 1 } { 2 } }$ 
A)  $4 x ^ { 2 } - 10 x + 18$ 
B)  $4 x ^ { 2 } + 10 x + 18$ 
C)  $4 x ^ { 2 } + 6 x + 10 + \frac { 18 } { x - \frac { 1 } { 2 } }$ 
D)  $4 x ^ { 2 } + 10 x + 18 - \frac { 18 } { x - \frac { 1 } { 2 } }$

Question 3

Multiply.
-$$( 5 x + 4 ) ( 4 x + 11 )$$

Accepted Answer

A)  $9 x ^ { 2 } + 71 x + 71$ 
B)  $20 x ^ { 2 } + 71 x + 44$ 
C)  $9 x ^ { 2 } + 71 x + 44$ 
D)  $20 x ^ { 2 } + 71 x + 71$ 
A)  $9 x ^ { 2 } + 71 x + 71$ 
B)  $20 x ^ { 2 } + 71 x + 44$ 
C)  $9 x ^ { 2 } + 71 x + 44$ 
D)  $20 x ^ { 2 } + 71 x + 71$

Question 4

Solve the equation.
-$$z ^ { 2 } + 3 z = z ( z - 9 )$$

Accepted Answer

A)  $\{ - 3,9 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ 3 , - 9 \}$ 
D)  $\varnothing$ 
A)  $\{ - 3,9 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ 3 , - 9 \}$ 
D)  $\varnothing$

Question 5

Multiply.
-$$( x - 5 ) ( x - 4 ) ( - 2 x - 1 )$$

Accepted Answer

A)  $- 2 x ^ { 3 } - 20$ 
B)  $- 2 x ^ { 3 } - 31 x ^ { 2 } + 17 x - 20$ 
C)  $- 2 x ^ { 3 } - 17 x ^ { 2 } + 31 x - 20$ 
D)  $- 2 x ^ { 3 } + 17 x ^ { 2 } - 31 x - 20$ 
A)  $- 2 x ^ { 3 } - 20$ 
B)  $- 2 x ^ { 3 } - 31 x ^ { 2 } + 17 x - 20$ 
C)  $- 2 x ^ { 3 } - 17 x ^ { 2 } + 31 x - 20$ 
D)  $- 2 x ^ { 3 } + 17 x ^ { 2 } - 31 x - 20$

Question 6

Divide.
-$\frac { - 40 x ^ { 8 } - 24 x ^ { 6 } - 16 x ^ { 4 } } { - 8 x ^ { 6 } }$

Accepted Answer

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

Question 7

Simplify the polynomial by combining like terms.
-$$\left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 x \right) + \left( 4 x ^ { 6 } - 3 x ^ { 5 } + 5 x \right)$$

Accepted Answer

A)  $11 x ^ { 6 } + 6 x ^ { 5 } + 9 x$ 
B)  $26 \mathrm { x } ^ { 12 }$ 
C)  $8 x ^ { 6 } + 4 x ^ { 5 } + 14 x$ 
D)  $11 x + 6 x ^ { 6 } + 9 x ^ { 5 }$ 
A)  $11 x ^ { 6 } + 6 x ^ { 5 } + 9 x$ 
B)  $26 \mathrm { x } ^ { 12 }$ 
C)  $8 x ^ { 6 } + 4 x ^ { 5 } + 14 x$ 
D)  $11 x + 6 x ^ { 6 } + 9 x ^ { 5 }$

Question 8

Simplify the polynomial by combining like terms.
-$\left( 8 x ^ { 2 } - x y - y ^ { 2 } \right)$ and $\left( x ^ { 2 } + 12 x y + 10 y ^ { 2 } \right)$

Accepted Answer

A)  $7 x ^ { 2 } - 13 x y - 11 y ^ { 2 }$ 
B)  $9 x ^ { 2 } + 11 x y + 9 y ^ { 2 }$ 
C)  $9 x ^ { 2 } + 13 x y + 11 y ^ { 2 }$ 
D)  $8 x ^ { 2 } + 12 x y + 10 y ^ { 2 }$ 
A)  $7 x ^ { 2 } - 13 x y - 11 y ^ { 2 }$ 
B)  $9 x ^ { 2 } + 11 x y + 9 y ^ { 2 }$ 
C)  $9 x ^ { 2 } + 13 x y + 11 y ^ { 2 }$ 
D)  $8 x ^ { 2 } + 12 x y + 10 y ^ { 2 }$

Question 9

Perform the indicated operation.
-$$\left( 10 x ^ { 3 } + 13 x ^ { 2 } + 6 x + 19 \right) \div ( 2 x + 1 )$$

Accepted Answer

A)  $5 x ^ { 2 } + 4 x + 1 + \frac { 18 } { 2 x + 1 }$ 
B)  $x ^ { 2 } + 1 + \frac { 21 } { 2 x + 1 }$ 
C)  $5 x ^ { 2 } + 4 x + 1$ 
D)  $5 x ^ { 2 } + 4 x + 1 + \frac { 21 } { 2 x + 1 }$ 
A)  $5 x ^ { 2 } + 4 x + 1 + \frac { 18 } { 2 x + 1 }$ 
B)  $x ^ { 2 } + 1 + \frac { 21 } { 2 x + 1 }$ 
C)  $5 x ^ { 2 } + 4 x + 1$ 
D)  $5 x ^ { 2 } + 4 x + 1 + \frac { 21 } { 2 x + 1 }$

Question 10

Solve the equation.
-$$x ( 3 x + 10 ) = 8$$

Accepted Answer

A)  $\left\{ \frac { 2 } { 3 } , - 4 \right\}$ 
B)  $\left\{ 0 , \frac { 10 } { 3 } \right\}$ 
C)  $\left\{ 0 , - \frac { 10 } { 3 } \right\}$ 
D)  $\{ 3,4 \}$ 
A)  $\left\{ \frac { 2 } { 3 } , - 4 \right\}$ 
B)  $\left\{ 0 , \frac { 10 } { 3 } \right\}$ 
C)  $\left\{ 0 , - \frac { 10 } { 3 } \right\}$ 
D)  $\{ 3,4 \}$

Question 11

Solve the problem.
-A pebble is hurled upward from the top of a 1040-foot-tall building with an initial velocity of 128 feet per second. Neglecting air resistance, the height h(t) in feet of the pebble after t seconds is given by the polynomial function $$h ( t ) = - 16 t ^ { 2 } + 128 t + 1040$$ a. Find the height of the pebble when $t = 1$.
b. Find the height of the pebble when $t = 5.1$.
c. Factor the polynomial $- 16 \mathrm { t } ^ { 2 } + 128 \mathrm { t } + 1040$.
d. When will the pebble hit the ground?

Accepted Answer

A)  a. $896 \mathrm { ft }$
b. $1276.64 \mathrm { ft }$
c. $- 16 ( t - 13 ) ( t + 5 )$
d. $13 \mathrm { sec }$ 
B)  a. $896 \mathrm { ft }$
b. $- 28.96 \mathrm { ft }$
c. $- 16 ( t + 13 ) ( t - 5 )$
d. $5 \mathrm { sec }$ 
C)  a. $1152 \mathrm { ft }$
b. $- 28.96 \mathrm { ft }$
c. $- 16 ( t + 13 ) ( t - 5 )$
d. $5 \mathrm { sec }$ 
D)  a. $1152 \mathrm { ft }$
b. $1276.64 \mathrm { ft }$
c. $- 16 ( t - 13 ) ( t + 5 )$
d. $13 \mathrm { sec }$ 
A)  a. $896 \mathrm { ft }$
b. $1276.64 \mathrm { ft }$
c. $- 16 ( t - 13 ) ( t + 5 )$
d. $13 \mathrm { sec }$ 
B)  a. $896 \mathrm { ft }$
b. $- 28.96 \mathrm { ft }$
c. $- 16 ( t + 13 ) ( t - 5 )$
d. $5 \mathrm { sec }$ 
C)  a. $1152 \mathrm { ft }$
b. $- 28.96 \mathrm { ft }$
c. $- 16 ( t + 13 ) ( t - 5 )$
d. $5 \mathrm { sec }$ 
D)  a. $1152 \mathrm { ft }$
b. $1276.64 \mathrm { ft }$
c. $- 16 ( t - 13 ) ( t + 5 )$
d. $13 \mathrm { sec }$

Question 12

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$$P ( x ) = - 2 x ^ { 2 } + 2 x + 5 ; - 3$$

Accepted Answer

A)  $- 19$ 
B)  29 
C)  $- 7$ 
D)  17 
A)  $- 19$ 
B)  29 
C)  $- 7$ 
D)  17

Question 13

Fill in the blank with one of the words or phrases listed below.

-The is the largest degree of all of its terms.

Accepted Answer

A) degree of a term 
B)  FOIL 
C)  binomial 
D)  degree of a polynomial 
A) degree of a term 
B)  FOIL 
C)  binomial 
D)  degree of a polynomial

Question 14

Factor the trinomial.
-$10 x ^ { 2 } - 23 x + 12$

Accepted Answer

A)  $( 2 x + 3 ) ( 5 x + 4 )$ 
B)  $( 2 x - 3 ) ( 5 x - 4 )$ 
C)  $( 10 x + 3 ) ( x + 4 )$ 
D)  prime polynomial 
A)  $( 2 x + 3 ) ( 5 x + 4 )$ 
B)  $( 2 x - 3 ) ( 5 x - 4 )$ 
C)  $( 10 x + 3 ) ( x + 4 )$ 
D)  prime polynomial

Question 15

Find the function.
-If $P ( x ) = 5 x + 2$, find $P ( x + h )$

Accepted Answer

A)  $5 x + h + 2$ 
B)  $5 x + 5 h + 2 h$ 
C)  $5 x + 5 h + 2$ 
D)  $x + h + 2$ 
A)  $5 x + h + 2$ 
B)  $5 x + 5 h + 2 h$ 
C)  $5 x + 5 h + 2$ 
D)  $x + h + 2$

Question 16

Solve the equation.
-$$x ^ { 2 } + 6 x - 40 = 0$$

Accepted Answer

A)  $\{ - 10,4 \}$ 
B)  $\{ 10,4 \}$ 
C)  $\{ 10 , - 4 \}$ 
D)  $\{ - 10,1 \}$ 
A)  $\{ - 10,4 \}$ 
B)  $\{ 10,4 \}$ 
C)  $\{ 10 , - 4 \}$ 
D)  $\{ - 10,1 \}$

Question 17

Factor the trinomial.
-$15 x ^ { 3 } - 14 x ^ { 2 } - 8 x$

Accepted Answer

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

Question 18

Divide.
-$\frac { 30 x ^ { 7 } y ^ { 7 } - 25 x ^ { 5 } y ^ { 5 } - 10 x ^ { 4 } y ^ { 4 } } { 5 x ^ { 4 } y ^ { 4 } }$

Accepted Answer

A)  $30 x ^ { 3 } y ^ { 3 } - 25 x y - 10$ 
B)  $6 x ^ { 3 } y ^ { 7 } - 5 x ^ { 4 } y ^ { 4 } - 2$ 
C)  $6 x ^ { 3 } y ^ { 3 } - 5 x y ^ { 5 } - 2$ 
D)  $6 x ^ { 3 } y ^ { 3 } - 5 x y - 2$ 
A)  $30 x ^ { 3 } y ^ { 3 } - 25 x y - 10$ 
B)  $6 x ^ { 3 } y ^ { 7 } - 5 x ^ { 4 } y ^ { 4 } - 2$ 
C)  $6 x ^ { 3 } y ^ { 3 } - 5 x y ^ { 5 } - 2$ 
D)  $6 x ^ { 3 } y ^ { 3 } - 5 x y - 2$

Question 19

Factor the polynomial.
-$$x ^ { 2 } + x - 20$$

Accepted Answer

A)  $( x - 5 ) ( x + 4 )$ 
B)  $( x + 1 ) ( x - 20 )$ 
C)  $( x - 4 ) ( x + 5 )$ 
D)  prime polynomial 
A)  $( x - 5 ) ( x + 4 )$ 
B)  $( x + 1 ) ( x - 20 )$ 
C)  $( x - 4 ) ( x + 5 )$ 
D)  prime polynomial

Question 20

Use synthetic division to divide.
-$$\frac { x ^ { 2 } + 2 x - 32 } { x + 7 }$$

Accepted Answer

A)  $x + 5 + \frac { 3 } { x + 7 }$ 
B)  $x - 3 + \frac { 5 } { x + 7 }$ 
C)  $x - 5 + \frac { 3 } { x + 7 }$ 
D)  $x - 5$ 
A)  $x + 5 + \frac { 3 } { x + 7 }$ 
B)  $x - 3 + \frac { 5 } { x + 7 }$ 
C)  $x - 5 + \frac { 3 } { x + 7 }$ 
D)  $x - 5$

Multiply. - $( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)$

Divide. - $\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 13 x - 9 } { x - \frac { 1 } { 2 } }$

Multiply. - $( 5 x + 4 ) ( 4 x + 11 )$

Solve the equation. - $z ^ { 2 } + 3 z = z ( z - 9 )$

Multiply. - $( x - 5 ) ( x - 4 ) ( - 2 x - 1 )$

Divide. - $\frac { - 40 x ^ { 8 } - 24 x ^ { 6 } - 16 x ^ { 4 } } { - 8 x ^ { 6 } }$

Simplify the polynomial by combining like terms. - $\left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 x \right) + \left( 4 x ^ { 6 } - 3 x ^ { 5 } + 5 x \right)$

Simplify the polynomial by combining like terms. - $\left( 8 x ^ { 2 } - x y - y ^ { 2 } \right)$ and $\left( x ^ { 2 } + 12 x y + 10 y ^ { 2 } \right)$

Perform the indicated operation. - $\left( 10 x ^ { 3 } + 13 x ^ { 2 } + 6 x + 19 \right) \div ( 2 x + 1 )$

Solve the equation. - $x ( 3 x + 10 ) = 8$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = - 2 x ^ { 2 } + 2 x + 5 ; - 3$

Fill in the blank with one of the words or phrases listed below. -The is the largest degree of all of its terms.

Factor the trinomial. - $10 x ^ { 2 } - 23 x + 12$

Find the function. -If $P ( x ) = 5 x + 2$ , find $P ( x + h )$

Solve the equation. - $x ^ { 2 } + 6 x - 40 = 0$

Factor the trinomial. - $15 x ^ { 3 } - 14 x ^ { 2 } - 8 x$

Divide. - $\frac { 30 x ^ { 7 } y ^ { 7 } - 25 x ^ { 5 } y ^ { 5 } - 10 x ^ { 4 } y ^ { 4 } } { 5 x ^ { 4 } y ^ { 4 } }$

Factor the polynomial. - $x ^ { 2 } + x - 20$

Use synthetic division to divide. - $\frac { x ^ { 2 } + 2 x - 32 } { x + 7 }$

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−5)(x+5)(x2+25)( x - 5 ) ( x + 5 ) \left( x ^ { 2 } + 25 \right)(x−5)(x+5)(x2+25)

Divide. - 4x3+8x2+13x−9x−12\frac { 4 x ^ { 3 } + 8 x ^ { 2 } + 13 x - 9 } { x - \frac { 1 } { 2 } }x−21​4x3+8x2+13x−9​

Multiply. - (5x+4)(4x+11)( 5 x + 4 ) ( 4 x + 11 )(5x+4)(4x+11)

Solve the equation. - z2+3z=z(z−9)z ^ { 2 } + 3 z = z ( z - 9 )z2+3z=z(z−9)

Multiply. - (x−5)(x−4)(−2x−1)( x - 5 ) ( x - 4 ) ( - 2 x - 1 )(x−5)(x−4)(−2x−1)

Divide. - −40x8−24x6−16x4−8x6\frac { - 40 x ^ { 8 } - 24 x ^ { 6 } - 16 x ^ { 4 } } { - 8 x ^ { 6 } }−8x6−40x8−24x6−16x4​

Simplify the polynomial by combining like terms. - (7x6+9x5+4x)+(4x6−3x5+5x)\left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 x \right) + \left( 4 x ^ { 6 } - 3 x ^ { 5 } + 5 x \right)(7x6+9x5+4x)+(4x6−3x5+5x)

Simplify the polynomial by combining like terms. - (8x2−xy−y2)\left( 8 x ^ { 2 } - x y - y ^ { 2 } \right)(8x2−xy−y2) and (x2+12xy+10y2)\left( x ^ { 2 } + 12 x y + 10 y ^ { 2 } \right)(x2+12xy+10y2)

Perform the indicated operation. - (10x3+13x2+6x+19)÷(2x+1)\left( 10 x ^ { 3 } + 13 x ^ { 2 } + 6 x + 19 \right) \div ( 2 x + 1 )(10x3+13x2+6x+19)÷(2x+1)

Solve the equation. - x(3x+10)=8x ( 3 x + 10 ) = 8x(3x+10)=8

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=−2x2+2x+5;−3P ( x ) = - 2 x ^ { 2 } + 2 x + 5 ; - 3P(x)=−2x2+2x+5;−3