Question 1

Factor the trinomial below. $u ^ { 2 } - 2 u v - 24 v ^ { 2 }$

Accepted Answer

A)  $( u + 4 v ) ( u + 6 v )$ 
B)  $( u - 4 v ) ( v - 6 u )$ 
C)  $( u - 4 v ) ( u - 6 v )$ 
D)  $( u + 4 v ) ( u - 6 v )$ 
E)  $( u - 4 v ) ( u + 6 v )$ 
A)  $( u + 4 v ) ( u + 6 v )$ 
B)  $( u - 4 v ) ( v - 6 u )$ 
C)  $( u - 4 v ) ( u - 6 v )$ 
D)  $( u + 4 v ) ( u - 6 v )$ 
E)  $( u - 4 v ) ( u + 6 v )$

Question 2

Find the sum $\left( - 9 x ^ { 2 } - 8 x + 12 \right) + \left( - 2 x ^ { 3 } - 5 x ^ { 2 } - 12 \right)$ .

Accepted Answer

A)  $- 2 x ^ { 3 } - 14 x ^ { 2 } - 8 x$ 
B)  $- 11 x ^ { 5 } - 13 x ^ { 3 }$ 
C)  $- 24 x ^ { 8 }$ 
D)  $- 11 x ^ { 5 } - 13 x ^ { 3 } + 24$ 
E)  $- 11 x ^ { 3 } - 13 x ^ { 2 } + 24$ 
A)  $- 2 x ^ { 3 } - 14 x ^ { 2 } - 8 x$ 
B)  $- 11 x ^ { 5 } - 13 x ^ { 3 }$ 
C)  $- 24 x ^ { 8 }$ 
D)  $- 11 x ^ { 5 } - 13 x ^ { 3 } + 24$ 
E)  $- 11 x ^ { 3 } - 13 x ^ { 2 } + 24$

Question 3

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. $\frac { s ^ { - 1 } + r ^ { - 1 } } { s ^ { - 1 } - r ^ { - 1 } }$

Accepted Answer

A)  $\frac { r - s } { r + s }$ 
B)  $s ^ { 2 } + r ^ { 2 }$ 
C)  $\frac { r + s } { r - s }$ 
D)  $\frac { s + r } { s - r }$ 
E)  $\frac { s - r } { s + r }$ 
A)  $\frac { r - s } { r + s }$ 
B)  $s ^ { 2 } + r ^ { 2 }$ 
C)  $\frac { r + s } { r - s }$ 
D)  $\frac { s + r } { s - r }$ 
E)  $\frac { s - r } { s + r }$

Question 4

Find the height in feet of a free-falling object at time t=0 using the function $s = - 16 t ^ { 2 } + 11 t + 30$ .

Accepted Answer

A) 30 feet 
B) 32 feet 
C) 22 feet 
D) 60 feet 
E) 16 feet 
A) 30 feet 
B) 32 feet 
C) 22 feet 
D) 60 feet 
E) 16 feet

Question 5

Factor out the greatest common monomial factor of the polynomial below, if one exists. $3 x ^ { 3 } y ^ { 3 } - 6 y$

Accepted Answer

A)  $3 y \left( x ^ { 3 } y ^ { 2 } - 2 \right)$ 
B)  $3 x \left( x ^ { 2 } y ^ { 3 } - 2 \right)$ 
C)  $3 x \left( x ^ { 3 } y ^ { 2 } - 2 \right)$ 
D)  $3 y \left( x ^ { 2 } y ^ { 3 } - 2 \right)$ 
E) no common factor other than 1 
A)  $3 y \left( x ^ { 3 } y ^ { 2 } - 2 \right)$ 
B)  $3 x \left( x ^ { 2 } y ^ { 3 } - 2 \right)$ 
C)  $3 x \left( x ^ { 3 } y ^ { 2 } - 2 \right)$ 
D)  $3 y \left( x ^ { 2 } y ^ { 3 } - 2 \right)$ 
E) no common factor other than 1

Question 6

Factor the trinomial, if possible. $12 x ^ { 2 } - 8 x - 15$

Accepted Answer

A)  $( 2 x - 3 ) ( 6 x - 5 )$ 
B)  $( 2 x + 3 ) ( 6 x + 5 )$ 
C)  $( 2 x - 3 ) ( 6 x + 5 )$ 
D)  $( 3 x + 2 ) ( 5 x - 6 )$ 
E) The trinomial is prime. 
A)  $( 2 x - 3 ) ( 6 x - 5 )$ 
B)  $( 2 x + 3 ) ( 6 x + 5 )$ 
C)  $( 2 x - 3 ) ( 6 x + 5 )$ 
D)  $( 3 x + 2 ) ( 5 x - 6 )$ 
E) The trinomial is prime.

Question 7

Find the value of  $\left( \frac { 6 } { 7 } \right) ^ { - 2 }$ .

Accepted Answer

A)  $- \frac { 49 } { 36 }$ 
B)  $\frac { 49 } { 36 }$ 
C)  $\frac { 36 } { 49 }$ 
D)  $\frac { 36 } { 7 }$ 
E)  - $\frac { 36 } { 49 }$ 
A)  $- \frac { 49 } { 36 }$ 
B)  $\frac { 49 } { 36 }$ 
C)  $\frac { 36 } { 49 }$ 
D)  $\frac { 36 } { 7 }$ 
E)  - $\frac { 36 } { 49 }$

Question 8

Perform the indicated operations and simplify. Assume that all exponents represent positive integers. $\left( - 2 x ^ { 3 n } + 2 x ^ { 2 n } - 4 x ^ { n } \right) - \left( 5 x ^ { 2 n } + 3 x ^ { n } - 2 \right)$

Accepted Answer

A)  $- 2 x ^ { 3 n } - 3 x ^ { 2 n } - 7 x ^ { n } + 2$ 
B)  $- 7 x ^ { 3 n } - 3 x ^ { 2 n } - 7 x ^ { n } + 2$ 
C)  $- 7 x ^ { 3 n } - x ^ { 2 n } - 2 x ^ { n } - 2$ 
D)  $- 2 x ^ { 3 n } + 7 x ^ { 2 n } - x ^ { n } - 2$ 
E)  $- 7 x ^ { 3 n } - x ^ { 2 n } - 2 x ^ { n }$ 
A)  $- 2 x ^ { 3 n } - 3 x ^ { 2 n } - 7 x ^ { n } + 2$ 
B)  $- 7 x ^ { 3 n } - 3 x ^ { 2 n } - 7 x ^ { n } + 2$ 
C)  $- 7 x ^ { 3 n } - x ^ { 2 n } - 2 x ^ { n } - 2$ 
D)  $- 2 x ^ { 3 n } + 7 x ^ { 2 n } - x ^ { n } - 2$ 
E)  $- 7 x ^ { 3 n } - x ^ { 2 n } - 2 x ^ { n }$

Question 9

Find the height in feet of a free-falling object at time t=4 using the function $s = - 16 t ^ { 2 } + 63 t + 144$ .

Accepted Answer

A) 652 feet 
B) 148 feet 
C) 4 feet 
D) 364 feet 
E) 140 feet 
A) 652 feet 
B) 148 feet 
C) 4 feet 
D) 364 feet 
E) 140 feet

Question 10

Fill in the missing factor. $7 x ^ { 2 } + 16 x + 4 = ( x + 2 ) ( \_ )$

Accepted Answer

A)  x+2 
B)  7x+2 
C)  x-2 
D)  7x-2 
E)  7x 
A)  x+2 
B)  7x+2 
C)  x-2 
D)  7x-2 
E)  7x

Question 11

Use a special product pattern to find the product $( x + 9 ) ( x - 9 )$ .

Accepted Answer

A)  $x ^ { 2 } - 18 x + 81$ 
B)  $x ^ { 2 } - 81$ 
C)  $x ^ { 2 } + 81$ 
D)  $x ^ { 2 } + 18 x + 81$ 
E)  $x ^ { 2 } - 18$ 
A)  $x ^ { 2 } - 18 x + 81$ 
B)  $x ^ { 2 } - 81$ 
C)  $x ^ { 2 } + 81$ 
D)  $x ^ { 2 } + 18 x + 81$ 
E)  $x ^ { 2 } - 18$

Question 12

An object is thrown upward from a height of 480 feet with an initial velocity of 16 feet per second. The height h (in feet)of the object after t seconds is modeled in the equation $h = - 16 t ^ { 2 } + 16 t + 480$ . How long will it take for the object to reach the ground?

Accepted Answer

A) 5 seconds 
B) 6 seconds 
C) 1 second 
D) 3 seconds 
E) 2 seconds 
A) 5 seconds 
B) 6 seconds 
C) 1 second 
D) 3 seconds 
E) 2 seconds

Question 13

Factor a negative real number out of the polynomial $10 - y ^ { 2 }$ and then write the polynomial factor in standard form.

Accepted Answer

A)  $10 - y ^ { 2 }$ 
B)  $- \left( y ^ { 2 } - 10 \right)$ 
C)  -($10 - y ^ { 2 }$  ) 
D)  $y ^ { 2 } + 10$ 
E)  -($y ^ { 2 } + 10$ ) 
A)  $10 - y ^ { 2 }$ 
B)  $- \left( y ^ { 2 } - 10 \right)$ 
C)  -($10 - y ^ { 2 }$  ) 
D)  $y ^ { 2 } + 10$ 
E)  -($y ^ { 2 } + 10$ )

Question 14

Factor the sum of cubes. $125 u ^ { 3 } + 1$

Accepted Answer

A)  $( 5 u - 1 ) \left( 25 u ^ { 2 } + 5 u + 1 \right)$ 
B)  $( 5 u + 1 ) \left( 25 u ^ { 2 } - 5 u + 1 \right)$ 
C)  $( 5 u - 1 ) \left( 25 u ^ { 2 } - 5 u + 1 \right)$ 
D)  $( 5 u + 1 ) \left( 25 u ^ { 2 } + 5 u - 1 \right)$ 
E)  $( 5 u + 1 ) \left( 25 u ^ { 2 } + 5 u + 1 \right)$ 
A)  $( 5 u - 1 ) \left( 25 u ^ { 2 } + 5 u + 1 \right)$ 
B)  $( 5 u + 1 ) \left( 25 u ^ { 2 } - 5 u + 1 \right)$ 
C)  $( 5 u - 1 ) \left( 25 u ^ { 2 } - 5 u + 1 \right)$ 
D)  $( 5 u + 1 ) \left( 25 u ^ { 2 } + 5 u - 1 \right)$ 
E)  $( 5 u + 1 ) \left( 25 u ^ { 2 } + 5 u + 1 \right)$

Question 15

Find all integers b such that the trinomial $x ^ { 2 } + b x + 10$ can be factored.

Accepted Answer

A)  $\pm 7 , \pm 11$ 
B)  10,1 
C)  $\pm 2 , \pm 5$ 
D)  -2,-5 
E)  -7,-11 
A)  $\pm 7 , \pm 11$ 
B)  10,1 
C)  $\pm 2 , \pm 5$ 
D)  -2,-5 
E)  -7,-11

Question 16

Find the sum of the polynomials. $\begin{array} { r } 
x ^ { 4 } + 9 x ^ { 3 } + 5 x + 7 \
8 x ^ { 3 } - 2 x - 7\
\hline
\end{array}$

Accepted Answer

A)  $x ^ { 4 } + 17 x ^ { 3 } + 3 x$ 
B)  $17 x ^ { 3 } + 3 x$ 
C)  $17 x ^ { 6 } + x ^ { 4 } + 3 x ^ { 2 }$ 
D)  $x ^ { 4 } + 17 x ^ { 3 } + 3 x + 14$ 
E)  $17 x ^ { 6 } + x ^ { 4 } + 3 x ^ { 2 } - 14$ 
A)  $x ^ { 4 } + 17 x ^ { 3 } + 3 x$ 
B)  $17 x ^ { 3 } + 3 x$ 
C)  $17 x ^ { 6 } + x ^ { 4 } + 3 x ^ { 2 }$ 
D)  $x ^ { 4 } + 17 x ^ { 3 } + 3 x + 14$ 
E)  $17 x ^ { 6 } + x ^ { 4 } + 3 x ^ { 2 } - 14$

Question 17

Use a special product pattern to find the product $[ 9 u + ( v + 10 ) ] ^ { 2 }$ .

Accepted Answer

A)  $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 100$ 
B)  $81 u ^ { 2 } + v ^ { 2 } + 20 v + 100$ 
C)  $81 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 100$ 
D)  $81 u ^ { 2 } + v ^ { 2 } + 100$ 
E)  $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 100$ 
A)  $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 100$ 
B)  $81 u ^ { 2 } + v ^ { 2 } + 20 v + 100$ 
C)  $81 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 100$ 
D)  $81 u ^ { 2 } + v ^ { 2 } + 100$ 
E)  $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 100$

Question 18

Multiply: $\left( - 7 y ^ { 4 } \right) \left( - 3 y ^ { 3 } \right)$

Accepted Answer

A)  $- 21 y ^ { 12 }$ 
B)  $- 10 y ^ { 7 }$ 
C)  $21 y ^ { 7 }$ 
D)  $- 10 y ^ { 12 }$ 
E)  $21 y ^ { 12 }$ 
A)  $- 21 y ^ { 12 }$ 
B)  $- 10 y ^ { 7 }$ 
C)  $21 y ^ { 7 }$ 
D)  $- 10 y ^ { 12 }$ 
E)  $21 y ^ { 12 }$

Question 19

Find the greatest common factor of the expressions $3 x ^ { 2 }$ and 9x .

Accepted Answer

A)  27x 
B)  $3 x ^ { 2 }$ 
C)  3x 
D)  $27 x ^ { 3 }$ 
E)  $9 x ^ { 2 }$ 
A)  27x 
B)  $3 x ^ { 2 }$ 
C)  3x 
D)  $27 x ^ { 3 }$ 
E)  $9 x ^ { 2 }$

Question 20

Use a special product pattern to find the product. $( u - ( v - 2 ) ) ( u + ( v - 2 ) )$

Accepted Answer

A)  $u ^ { 2 } + ( v - 2 ) ^ { 2 }$ 
B)  $u ^ { 2 } - ( v - 2 ) ^ { 2 }$ 
C)  $u ^ { 2 } - 2 u ( v - 2 ) + ( v - 2 ) ^ { 2 }$ 
D)  $u ^ { 2 } - 2 u ( v - 2 ) - ( v - 2 ) ^ { 2 }$ 
E)  $u ^ { 2 } + 2 u ( v - 2 ) - ( v - 2 ) ^ { 2 }$ 
A)  $u ^ { 2 } + ( v - 2 ) ^ { 2 }$ 
B)  $u ^ { 2 } - ( v - 2 ) ^ { 2 }$ 
C)  $u ^ { 2 } - 2 u ( v - 2 ) + ( v - 2 ) ^ { 2 }$ 
D)  $u ^ { 2 } - 2 u ( v - 2 ) - ( v - 2 ) ^ { 2 }$ 
E)  $u ^ { 2 } + 2 u ( v - 2 ) - ( v - 2 ) ^ { 2 }$

Factor the trinomial below. $u ^ { 2 } - 2 u v - 24 v ^ { 2 }$

Find the sum $\left( - 9 x ^ { 2 } - 8 x + 12 \right) + \left( - 2 x ^ { 3 } - 5 x ^ { 2 } - 12 \right)$ .

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. $\frac { s ^ { - 1 } + r ^ { - 1 } } { s ^ { - 1 } - r ^ { - 1 } }$

Find the height in feet of a free-falling object at time t=0 using the function $s = - 16 t ^ { 2 } + 11 t + 30$ .

Factor out the greatest common monomial factor of the polynomial below, if one exists. $3 x ^ { 3 } y ^ { 3 } - 6 y$

Factor the trinomial, if possible. $12 x ^ { 2 } - 8 x - 15$

Find the value of $\left( \frac { 6 } { 7 } \right) ^ { - 2 }$ .

Perform the indicated operations and simplify. Assume that all exponents represent positive integers. $\left( - 2 x ^ { 3 n } + 2 x ^ { 2 n } - 4 x ^ { n } \right) - \left( 5 x ^ { 2 n } + 3 x ^ { n } - 2 \right)$

Find the height in feet of a free-falling object at time t=4 using the function $s = - 16 t ^ { 2 } + 63 t + 144$ .

Fill in the missing factor. $7 x ^ { 2 } + 16 x + 4 = ( x + 2 ) ( \_ )$

Use a special product pattern to find the product $( x + 9 ) ( x - 9 )$ .

An object is thrown upward from a height of 480 feet with an initial velocity of 16 feet per second. The height h (in feet)of the object after t seconds is modeled in the equation $h = - 16 t ^ { 2 } + 16 t + 480$ . How long will it take for the object to reach the ground?

Factor a negative real number out of the polynomial $10 - y ^ { 2 }$ and then write the polynomial factor in standard form.

Factor the sum of cubes. $125 u ^ { 3 } + 1$

Find all integers b such that the trinomial $x ^ { 2 } + b x + 10$ can be factored.

Find the sum of the polynomials. +9+5x+7 8-2x-7

Use a special product pattern to find the product $[ 9 u + ( v + 10 ) ] ^ { 2 }$ .

Multiply: $\left( - 7 y ^ { 4 } \right) \left( - 3 y ^ { 3 } \right)$

Find the greatest common factor of the expressions $3 x ^ { 2 }$ and 9x .

Use a special product pattern to find the product. $( u - ( v - 2 ) ) ( u + ( v - 2 ) )$

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

Factor the trinomial below. u2−2uv−24v2u ^ { 2 } - 2 u v - 24 v ^ { 2 }u2−2uv−24v2

Find the sum (−9x2−8x+12)+(−2x3−5x2−12)\left( - 9 x ^ { 2 } - 8 x + 12 \right) + \left( - 2 x ^ { 3 } - 5 x ^ { 2 } - 12 \right)(−9x2−8x+12)+(−2x3−5x2−12) .

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. s−1+r−1s−1−r−1\frac { s ^ { - 1 } + r ^ { - 1 } } { s ^ { - 1 } - r ^ { - 1 } }s−1−r−1s−1+r−1​

Find the height in feet of a free-falling object at time t=0 using the function s=−16t2+11t+30s = - 16 t ^ { 2 } + 11 t + 30s=−16t2+11t+30 .

Factor out the greatest common monomial factor of the polynomial below, if one exists. 3x3y3−6y3 x ^ { 3 } y ^ { 3 } - 6 y3x3y3−6y

Factor the trinomial, if possible. 12x2−8x−1512 x ^ { 2 } - 8 x - 1512x2−8x−15

Find the value of (67)−2\left( \frac { 6 } { 7 } \right) ^ { - 2 }(76​)−2 .

Perform the indicated operations and simplify. Assume that all exponents represent positive integers. (−2x3n+2x2n−4xn)−(5x2n+3xn−2)\left( - 2 x ^ { 3 n } + 2 x ^ { 2 n } - 4 x ^ { n } \right) - \left( 5 x ^ { 2 n } + 3 x ^ { n } - 2 \right)(−2x3n+2x2n−4xn)−(5x2n+3xn−2)

Find the height in feet of a free-falling object at time t=4 using the function s=−16t2+63t+144s = - 16 t ^ { 2 } + 63 t + 144s=−16t2+63t+144 .

Fill in the missing factor. 7x2+16x+4=(x+2)(_)7 x ^ { 2 } + 16 x + 4 = ( x + 2 ) ( \_ )7x2+16x+4=(x+2)(_)

Use a special product pattern to find the product (x+9)(x−9)( x + 9 ) ( x - 9 )(x+9)(x−9) .

Factor a negative real number out of the polynomial 10−y210 - y ^ { 2 }10−y2 and then write the polynomial factor in standard form.

Factor the sum of cubes. 125u3+1125 u ^ { 3 } + 1125u3+1

Find all integers b such that the trinomial x2+bx+10x ^ { 2 } + b x + 10x2+bx+10 can be factored.

Find the sum of the polynomials. +9+5x+7 8-2x-7

Use a special product pattern to find the product [9u+(v+10)]2[ 9 u + ( v + 10 ) ] ^ { 2 }[9u+(v+10)]2 .

Multiply: (−7y4)(−3y3)\left( - 7 y ^ { 4 } \right) \left( - 3 y ^ { 3 } \right)(−7y4)(−3y3)

Find the greatest common factor of the expressions 3x23 x ^ { 2 }3x2 and 9x .

Use a special product pattern to find the product. (u−(v−2))(u+(v−2))( u - ( v - 2 ) ) ( u + ( v - 2 ) )(u−(v−2))(u+(v−2))

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

Factor the trinomial below. $u ^ { 2 } - 2 u v - 24 v ^ { 2 }$

Find the sum $\left( - 9 x ^ { 2 } - 8 x + 12 \right) + \left( - 2 x ^ { 3 } - 5 x ^ { 2 } - 12 \right)$ .

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. $\frac { s ^ { - 1 } + r ^ { - 1 } } { s ^ { - 1 } - r ^ { - 1 } }$

Find the height in feet of a free-falling object at time t=0 using the function $s = - 16 t ^ { 2 } + 11 t + 30$ .

Factor out the greatest common monomial factor of the polynomial below, if one exists. $3 x ^ { 3 } y ^ { 3 } - 6 y$

Factor the trinomial, if possible. $12 x ^ { 2 } - 8 x - 15$

Find the value of $\left( \frac { 6 } { 7 } \right) ^ { - 2 }$ .

Perform the indicated operations and simplify. Assume that all exponents represent positive integers. $\left( - 2 x ^ { 3 n } + 2 x ^ { 2 n } - 4 x ^ { n } \right) - \left( 5 x ^ { 2 n } + 3 x ^ { n } - 2 \right)$

Find the height in feet of a free-falling object at time t=4 using the function $s = - 16 t ^ { 2 } + 63 t + 144$ .

Fill in the missing factor. $7 x ^ { 2 } + 16 x + 4 = ( x + 2 ) ( \_ )$

Use a special product pattern to find the product $( x + 9 ) ( x - 9 )$ .

Factor a negative real number out of the polynomial $10 - y ^ { 2 }$ and then write the polynomial factor in standard form.

Factor the sum of cubes. $125 u ^ { 3 } + 1$

Find all integers b such that the trinomial $x ^ { 2 } + b x + 10$ can be factored.

Use a special product pattern to find the product $[ 9 u + ( v + 10 ) ] ^ { 2 }$ .

Multiply: $\left( - 7 y ^ { 4 } \right) \left( - 3 y ^ { 3 } \right)$

Find the greatest common factor of the expressions $3 x ^ { 2 }$ and 9x .

Use a special product pattern to find the product. $( u - ( v - 2 ) ) ( u + ( v - 2 ) )$