Question 1

Simplify the polynomial by combining like terms.
-$$- 5 x ^ { 2 } + 4 x + 3 x + 5 x$$

Accepted Answer

A)  $- 300 x ^ { 5 }$ 
B)  $- 5 x ^ { 2 } + 7 x$ 
C)  $- 5 x ^ { 2 } + 7 x + 5$ 
D)  $- 5 x ^ { 2 } + 12 x$ 
A)  $- 300 x ^ { 5 }$ 
B)  $- 5 x ^ { 2 } + 7 x$ 
C)  $- 5 x ^ { 2 } + 7 x + 5$ 
D)  $- 5 x ^ { 2 } + 12 x$

Question 2

Simplify the polynomial by combining like terms.
-$$\left( \frac { 2 } { 5 } x ^ { 2 } + \frac { 2 } { 5 } x + \frac { 3 } { 4 } \right) + \left( \frac { 4 } { 5 } x ^ { 2 } - \frac { 3 } { 4 } x + \frac { 1 } { 4 } \right)$$

Accepted Answer

A)  $\frac { 6 } { 5 } x ^ { 4 } - \frac { 7 } { 20 } x ^ { 2 } + 1$ 
B)  $\frac { 6 } { 5 } x ^ { 2 } - \frac { 7 } { 20 } x - 1$ 
C)  $\frac { 6 } { 5 } x ^ { 2 } - \frac { 7 } { 20 } x + 1$ 
D)  $\frac { 17 } { 20 } x ^ { 6 } + 1$ 
A)  $\frac { 6 } { 5 } x ^ { 4 } - \frac { 7 } { 20 } x ^ { 2 } + 1$ 
B)  $\frac { 6 } { 5 } x ^ { 2 } - \frac { 7 } { 20 } x - 1$ 
C)  $\frac { 6 } { 5 } x ^ { 2 } - \frac { 7 } { 20 } x + 1$ 
D)  $\frac { 17 } { 20 } x ^ { 6 } + 1$

Question 3

Factor the polynomial by grouping.
-$3 b c - 15 b + 8 c - 40$

Accepted Answer

A)  $( 3 b + 8 c ) ( c - 5 )$ 
B)  $( 3 b + 8 ) ( c - 5 )$ 
C)  $( 3 b + c ) ( 8 c - 5 )$ 
D)  $( 3 b - 5 ) ( c + 8 )$ 
A)  $( 3 b + 8 c ) ( c - 5 )$ 
B)  $( 3 b + 8 ) ( c - 5 )$ 
C)  $( 3 b + c ) ( 8 c - 5 )$ 
D)  $( 3 b - 5 ) ( c + 8 )$

Question 4

Solve.
-One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Accepted Answer

A)  25 in., 60 in., 65 in. 
B)  20 in., 55 in., 60 in 
C)  26 in., 61 in., 66 in 
D)  24 in., 59 in., 66 in 
A)  25 in., 60 in., 65 in. 
B)  20 in., 55 in., 60 in 
C)  26 in., 61 in., 66 in 
D)  24 in., 59 in., 66 in

Question 5

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

-A is a finite sum of terms in which all variables are raised to nonnegative integer powers and no variables appear in any denominator.

Accepted Answer

A)  monomial 
B)  binomial 
C)  quadratic equation 
D)  polynomial 
A)  monomial 
B)  binomial 
C)  quadratic equation 
D)  polynomial

Question 6

Factor the polynomial completely.
-$$( x + 1 ) ^ { 2 } + 16 ( x + 1 ) + 64$$

Accepted Answer

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

Question 7

Factor out the greatest common factor. Assume that variables used as exponents represent positive integers.
-$$14 x ^ { 3 a } - 4 x ^ { 2 a } + 10 x ^ { a }$$

Accepted Answer

A)  $2 x ^ { a } \left( 7 x ^ { 2 a } - 2 x ^ { a } + 5 \right)$ 
B)  $x ^ { a } \left( 14 x ^ { 2 a } - 4 x ^ { a } + 10 \right)$ 
C)  $2 \left( 7 x ^ { 3 a } - 2 x ^ { 2 a } + 5 x ^ { a } \right)$ 
D)  $2 x ^ { a } \left( 7 x ^ { 3 a } - 2 x ^ { 2 a } + 5 x ^ { a } \right)$ 
A)  $2 x ^ { a } \left( 7 x ^ { 2 a } - 2 x ^ { a } + 5 \right)$ 
B)  $x ^ { a } \left( 14 x ^ { 2 a } - 4 x ^ { a } + 10 \right)$ 
C)  $2 \left( 7 x ^ { 3 a } - 2 x ^ { 2 a } + 5 x ^ { a } \right)$ 
D)  $2 x ^ { a } \left( 7 x ^ { 3 a } - 2 x ^ { 2 a } + 5 x ^ { a } \right)$

Question 8

Factor completely.
-$343 x ^ { 3 } + y ^ { 3 }$

Accepted Answer

A)  $( 7 x + y ) \left( 49 x ^ { 2 } + 7 x y + y ^ { 2 } \right)$ 
B)  $( 7 x + y ) \left( 49 x ^ { 2 } - 7 x y + y ^ { 2 } \right)$ 
C)  $( 7 x + y ) \left( 49 x ^ { 2 } + y ^ { 2 } \right)$ 
D)  $( 7 x - y ) \left( 49 x ^ { 2 } + 7 x y + y ^ { 2 } \right)$ 
A)  $( 7 x + y ) \left( 49 x ^ { 2 } + 7 x y + y ^ { 2 } \right)$ 
B)  $( 7 x + y ) \left( 49 x ^ { 2 } - 7 x y + y ^ { 2 } \right)$ 
C)  $( 7 x + y ) \left( 49 x ^ { 2 } + y ^ { 2 } \right)$ 
D)  $( 7 x - y ) \left( 49 x ^ { 2 } + 7 x y + y ^ { 2 } \right)$

Question 9

Solve the equation.
-$$x ^ { 3 } - x = - 6 x ^ { 2 } + 6$$

Accepted Answer

A)  $\{ 36 \}$ 
B)  $\{ - 1,1 , - 6 \}$ 
C)  $\{ 1 , - 6,6 \}$ 
D)  $\{ - 6,6 \}$ 
A)  $\{ 36 \}$ 
B)  $\{ - 1,1 , - 6 \}$ 
C)  $\{ 1 , - 6,6 \}$ 
D)  $\{ - 6,6 \}$

Question 10

Factor.
-$250 x ^ { 3 } + 128$

Accepted Answer

A)  $2 ( 5 x + 4 ) \left( 25 x ^ { 2 } + 16 \right)$ 
B)  $2 \left( 125 x ^ { 3 } + 64 \right)$ 
C)  $2 ( 5 x - 4 ) \left( 25 x ^ { 2 } + 20 x + 16 \right)$ 
D)  $2 ( 5 x + 4 ) \left( 25 x ^ { 2 } - 20 x + 16 \right)$ 
A)  $2 ( 5 x + 4 ) \left( 25 x ^ { 2 } + 16 \right)$ 
B)  $2 \left( 125 x ^ { 3 } + 64 \right)$ 
C)  $2 ( 5 x - 4 ) \left( 25 x ^ { 2 } + 20 x + 16 \right)$ 
D)  $2 ( 5 x + 4 ) \left( 25 x ^ { 2 } - 20 x + 16 \right)$

Question 11

Factor out the greatest common factor.
-$$15 ( y + 7 ) - x ( y + 7 )$$

Accepted Answer

A)  $( 15 y + 105 ) - ( x y + 7 x )$ 
B)  $( y + 7 ) ( 15 - x )$ 
C)  $( y - 7 ) ( x - 15 )$ 
D)  $( y + 7 ) ( 15 + x )$ 
A)  $( 15 y + 105 ) - ( x y + 7 x )$ 
B)  $( y + 7 ) ( 15 - x )$ 
C)  $( y - 7 ) ( x - 15 )$ 
D)  $( y + 7 ) ( 15 + x )$

Question 12

Factor out the greatest common factor.
-$$x \left( x ^ { 2 } + 11 \right) - 14 \left( x ^ { 2 } + 11 \right)$$

Accepted Answer

A)  $\left( x ^ { 2 } + 11 \right) ( x - 14 )$ 
B)  $\left( x ^ { 3 } + 11 x \right) - \left( 14 x ^ { 2 } + 154 \right)$ 
C)  $\left( x ^ { 2 } + 11 \right) ( x + 14 )$ 
D)  $- 14 x \left( x ^ { 2 } + 11 \right)$ 
A)  $\left( x ^ { 2 } + 11 \right) ( x - 14 )$ 
B)  $\left( x ^ { 3 } + 11 x \right) - \left( 14 x ^ { 2 } + 154 \right)$ 
C)  $\left( x ^ { 2 } + 11 \right) ( x + 14 )$ 
D)  $- 14 x \left( x ^ { 2 } + 11 \right)$

Question 13

For the given f(x $$f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$$
-$$f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } + 7 x - 8 ; g ( x ) = x - 1$$

Accepted Answer

A)  $x ^ { 3 } - 2 x ^ { 2 } - x + 6 - \frac { 2 } { x - 1 } ; x \neq - 1$ 
B)  $x ^ { 3 } - 2 x ^ { 2 } + x + 6 + \frac { 4 } { x - 1 } ; x \neq 1$ 
C)  $x ^ { 3 } - 2 x ^ { 2 } + x + 8 + \frac { 4 } { x - 1 } ; x \neq 1$ 
D)  $x ^ { 3 } - 2 x ^ { 2 } - x + 6 - \frac { 2 } { x - 1 } ; x \neq 1$ 
A)  $x ^ { 3 } - 2 x ^ { 2 } - x + 6 - \frac { 2 } { x - 1 } ; x \neq - 1$ 
B)  $x ^ { 3 } - 2 x ^ { 2 } + x + 6 + \frac { 4 } { x - 1 } ; x \neq 1$ 
C)  $x ^ { 3 } - 2 x ^ { 2 } + x + 8 + \frac { 4 } { x - 1 } ; x \neq 1$ 
D)  $x ^ { 3 } - 2 x ^ { 2 } - x + 6 - \frac { 2 } { x - 1 } ; x \neq 1$

Question 14

Factor the polynomial completely.
-$$a ^ { 2 } + 3 a b - 28 b ^ { 2 }$$

Accepted Answer

A)  $( a - 7 b ) ( a + b )$ 
B)  $( a - b ) ( a + 4 b )$ 
C)  $( a - 7 b ) ( a + 4 b )$ 
D)  $( a + 7 b ) ( a - 4 b )$ 
A)  $( a - 7 b ) ( a + b )$ 
B)  $( a - b ) ( a + 4 b )$ 
C)  $( a - 7 b ) ( a + 4 b )$ 
D)  $( a + 7 b ) ( a - 4 b )$

Question 15

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$$P ( x ) = 4 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - x - 4 ; \frac { 1 } { 2 }$$

Accepted Answer

A)  $\frac { 17 } { 4 }$ 
B)  $- 4$ 
C)  4 
D)  $- \frac { 17 } { 4 }$ 
A)  $\frac { 17 } { 4 }$ 
B)  $- 4$ 
C)  4 
D)  $- \frac { 17 } { 4 }$

Question 16

Use synthetic division to divide.
-$$\frac { x ^ { 2 } + 13 x + 30 } { x + 3 }$$

Accepted Answer

A)  $x + 10$ 
B)  $x + 30$ 
C)  $x - 10$ 
D)  $x + 3$ 
A)  $x + 10$ 
B)  $x + 30$ 
C)  $x - 10$ 
D)  $x + 3$

Question 17

Solve.
-A flagpole is supported by a wire fastened 27 feet from its base. The wire is 9 feet longer than the height it reaches on the flagpole. Find the length of the wire.

Accepted Answer

A)  32 ft 
B)  45 ft 
C)  51 ft 
D)  36 ft 
A)  32 ft 
B)  45 ft 
C)  51 ft 
D)  36 ft

Question 18

Factor the polynomial.
-$15 x ^ { 2 } - 9 x y - 20 x + 12 y$

Accepted Answer

A)  $( 3 x - 4 y ) ( 5 x - 3 )$ 
B)  $( 3 x - 4 y ) ( 5 x - 3 y )$ 
C)  $( 3 x - 4 ) ( 5 x - 3 )$ 
D)  (3x - 4)(5x - 3y) 
A)  $( 3 x - 4 y ) ( 5 x - 3 )$ 
B)  $( 3 x - 4 y ) ( 5 x - 3 y )$ 
C)  $( 3 x - 4 ) ( 5 x - 3 )$ 
D)  (3x - 4)(5x - 3y)

Question 19

Perform the indicated operation.
-$$\left( 9 x ^ { 7 } + 3 x ^ { 6 } - 19 \right) - \left( 5 x ^ { 7 } - 4 x ^ { 6 } - 3 \right)$$

Accepted Answer

A)  $4 x ^ { 7 } + 7 x ^ { 6 } - 22$ 
B)  $- 5 x ^ { 13 }$ 
C)  $4 x ^ { 7 } + 8 x ^ { 6 } - 22$ 
D)  $4 x ^ { 7 } + 7 x ^ { 6 } - 16$ 
A)  $4 x ^ { 7 } + 7 x ^ { 6 } - 22$ 
B)  $- 5 x ^ { 13 }$ 
C)  $4 x ^ { 7 } + 8 x ^ { 6 } - 22$ 
D)  $4 x ^ { 7 } + 7 x ^ { 6 } - 16$

Question 20

Use synthetic division to divide.
-$$\frac { 7 x ^ { 2 } + 11 x - 6 } { x + 2 }$$

Accepted Answer

A)  $- 7 x + 3$ 
B)  $x - 3$ 
C)  $- 3 x + 2$ 
D)  $7 x - 3$ 
A)  $- 7 x + 3$ 
B)  $x - 3$ 
C)  $- 3 x + 2$ 
D)  $7 x - 3$

Simplify the polynomial by combining like terms. - $- 5 x ^ { 2 } + 4 x + 3 x + 5 x$

Simplify the polynomial by combining like terms. - $\left( \frac { 2 } { 5 } x ^ { 2 } + \frac { 2 } { 5 } x + \frac { 3 } { 4 } \right) + \left( \frac { 4 } { 5 } x ^ { 2 } - \frac { 3 } { 4 } x + \frac { 1 } { 4 } \right)$

Factor the polynomial by grouping. - $3 b c - 15 b + 8 c - 40$

Solve. -One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Fill in the blank with one of the words or phrases listed below. -A is a finite sum of terms in which all variables are raised to nonnegative integer powers and no variables appear in any denominator.

Factor the polynomial completely. - $( x + 1 ) ^ { 2 } + 16 ( x + 1 ) + 64$

Factor out the greatest common factor. Assume that variables used as exponents represent positive integers. - $14 x ^ { 3 a } - 4 x ^ { 2 a } + 10 x ^ { a }$

Factor completely. - $343 x ^ { 3 } + y ^ { 3 }$

Solve the equation. - $x ^ { 3 } - x = - 6 x ^ { 2 } + 6$

Factor. - $250 x ^ { 3 } + 128$

Factor out the greatest common factor. - $15 ( y + 7 ) - x ( y + 7 )$

Factor out the greatest common factor. - $x \left( x ^ { 2 } + 11 \right) - 14 \left( x ^ { 2 } + 11 \right)$

For the given f(x $f ( x ) \text { and } g ( x ) \text {, find } \frac { f ( x ) } { g ( x ) } \text {. Also find any } x \text {-values that are not in the domain of } \frac { f ( x ) } { g ( x ) }$ - $f ( x ) = x ^ { 4 } - 3 x ^ { 3 } + x ^ { 2 } + 7 x - 8 ; g ( x ) = x - 1$

Factor the polynomial completely. - $a ^ { 2 } + 3 a b - 28 b ^ { 2 }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = 4 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - x - 4 ; \frac { 1 } { 2 }$

Use synthetic division to divide. - $\frac { x ^ { 2 } + 13 x + 30 } { x + 3 }$

Solve. -A flagpole is supported by a wire fastened 27 feet from its base. The wire is 9 feet longer than the height it reaches on the flagpole. Find the length of the wire.

Factor the polynomial. - $15 x ^ { 2 } - 9 x y - 20 x + 12 y$

Perform the indicated operation. - $\left( 9 x ^ { 7 } + 3 x ^ { 6 } - 19 \right) - \left( 5 x ^ { 7 } - 4 x ^ { 6 } - 3 \right)$

Use synthetic division to divide. - $\frac { 7 x ^ { 2 } + 11 x - 6 } { x + 2 }$

Real Numbers and Algebraic Expressions

Equations, Inequalities, and Problem Solving

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Exam 5: Polynomials and Polynomial Functions

Simplify the polynomial by combining like terms. - −5x2+4x+3x+5x- 5 x ^ { 2 } + 4 x + 3 x + 5 x−5x2+4x+3x+5x

Simplify the polynomial by combining like terms. - (25x2+25x+34)+(45x2−34x+14)\left( \frac { 2 } { 5 } x ^ { 2 } + \frac { 2 } { 5 } x + \frac { 3 } { 4 } \right) + \left( \frac { 4 } { 5 } x ^ { 2 } - \frac { 3 } { 4 } x + \frac { 1 } { 4 } \right)(52​x2+52​x+43​)+(54​x2−43​x+41​)

Factor the polynomial by grouping. - 3bc−15b+8c−403 b c - 15 b + 8 c - 403bc−15b+8c−40

Solve. -One leg of a right triangle is 35 inches longer than the smaller leg, and the hypotenuse is 40 inches longer than the smaller leg. Find the lengths of the sides of the triangle.

Fill in the blank with one of the words or phrases listed below. -A is a finite sum of terms in which all variables are raised to nonnegative integer powers and no variables appear in any denominator.

Factor the polynomial completely. - (x+1)2+16(x+1)+64( x + 1 ) ^ { 2 } + 16 ( x + 1 ) + 64(x+1)2+16(x+1)+64

Factor out the greatest common factor. Assume that variables used as exponents represent positive integers. - 14x3a−4x2a+10xa14 x ^ { 3 a } - 4 x ^ { 2 a } + 10 x ^ { a }14x3a−4x2a+10xa

Factor completely. - 343x3+y3343 x ^ { 3 } + y ^ { 3 }343x3+y3

Solve the equation. - x3−x=−6x2+6x ^ { 3 } - x = - 6 x ^ { 2 } + 6x3−x=−6x2+6

Factor. - 250x3+128250 x ^ { 3 } + 128250x3+128

Factor out the greatest common factor. - 15(y+7)−x(y+7)15 ( y + 7 ) - x ( y + 7 )15(y+7)−x(y+7)

Factor out the greatest common factor. - x(x2+11)−14(x2+11)x \left( x ^ { 2 } + 11 \right) - 14 \left( x ^ { 2 } + 11 \right)x(x2+11)−14(x2+11)

Factor the polynomial completely. - a2+3ab−28b2a ^ { 2 } + 3 a b - 28 b ^ { 2 }a2+3ab−28b2

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=4x4−2x3+x2−x−4;12P ( x ) = 4 x ^ { 4 } - 2 x ^ { 3 } + x ^ { 2 } - x - 4 ; \frac { 1 } { 2 }P(x)=4x4−2x3+x2−x−4;21​

Use synthetic division to divide. - x2+13x+30x+3\frac { x ^ { 2 } + 13 x + 30 } { x + 3 }x+3x2+13x+30​