Question 1

Solve the equation below by factoring. $x ^ { 2 } - 49 = 0$

Accepted Answer

A)  $x = - 7$ and $x = 7$ 
B)  $x = 7$ 
C)  $x = - 7$ 
D)  $x = 0$ and $x = 7$ 
E)  $x = - 7$ and $x = 0$ 
A)  $x = - 7$ and $x = 7$ 
B)  $x = 7$ 
C)  $x = - 7$ 
D)  $x = 0$ and $x = 7$ 
E)  $x = - 7$ and $x = 0$ A

Question 2

The open box with a square base is to be constructed from 1056 square inches of material. The height of the box is 5 inches. Find the dimensions of the base.

Accepted Answer

A) 34 inches by 34 inches 
B) 24 inches by 24 inches 
C) 44 inches by 44 inches 
D) 14 inches by 14 inches 
E) 39 inches by 39 inches 
A) 34 inches by 34 inches 
B) 24 inches by 24 inches 
C) 44 inches by 44 inches 
D) 14 inches by 14 inches 
E) 39 inches by 39 inches B

Question 3

Simplify the expression $\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }$ . Assume that neither u nor v is zero.

Accepted Answer

A)  $\frac { 2 v ^ { 2 } } { 25 u ^ { 2 } }$ 
B)  $\frac { 2 v ^ { 2 } } { 25 }$ 
C)  $\frac { 2 v ^ { 4 } } { 5 u ^ { 2 } }$ 
D)  $\frac { 2 v } { 5 }$ 
E)  $\frac { 2 } { v ^ { 2 } }$ 
A)  $\frac { 2 v ^ { 2 } } { 25 u ^ { 2 } }$ 
B)  $\frac { 2 v ^ { 2 } } { 25 }$ 
C)  $\frac { 2 v ^ { 4 } } { 5 u ^ { 2 } }$ 
D)  $\frac { 2 v } { 5 }$ 
E)  $\frac { 2 } { v ^ { 2 } }$ B

Question 4

Solve the equation below by factoring. $x ^ { 2 } - 4 x - 45 = 0$

Accepted Answer

A)  $5 , - 9$ 
B)  $- 5,9$ 
C)  $4,5$ 
D)  $0,9$ 
E)  $- 5 , - 9$ 
A)  $5 , - 9$ 
B)  $- 5,9$ 
C)  $4,5$ 
D)  $0,9$ 
E)  $- 5 , - 9$

Question 5

Evaluate the expression $\left( 9 + 3 ^ { - 4 } \right) ^ { 0 }$ .

Accepted Answer

A)  $\frac { 730 } { 81 }$ 
B) 0 
C)  9 
D) 1 
E)  $\frac { 1 } { 81 }$ 
A)  $\frac { 730 } { 81 }$ 
B) 0 
C)  9 
D) 1 
E)  $\frac { 1 } { 81 }$

Question 6

Find the difference $\left( 9 x ^ { 2 } + 4 x - 10 \right) - \left( 4 x + 9 x ^ { 2 } - 10 \right)$ .

Accepted Answer

A) -20 
B) 0 
C)  $8 x - 20$ 
D)  $18 x - 20$ 
E)  $8 x ^ { 2 } + 8 x - 20$ 
A) -20 
B) 0 
C)  $8 x - 20$ 
D)  $18 x - 20$ 
E)  $8 x ^ { 2 } + 8 x - 20$

Question 7

Simplify the expression $( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 }$ .

Accepted Answer

A)  $s ^ { 44 } t ^ { 32 }$ 
B)  $s ^ { 37 } t ^ { 16 }$ 
C)  $s ^ { 16 } t ^ { 10 }$ 
D)  $s ^ { 96 } t ^ { 16 }$ 
E)  $s ^ { 20 } t ^ { 10 }$ 
A)  $s ^ { 44 } t ^ { 32 }$ 
B)  $s ^ { 37 } t ^ { 16 }$ 
C)  $s ^ { 16 } t ^ { 10 }$ 
D)  $s ^ { 96 } t ^ { 16 }$ 
E)  $s ^ { 20 } t ^ { 10 }$

Question 8

Factor the trinomial by grouping, if possible. $10 x ^ { 2 } - 9 x - 9$

Accepted Answer

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

Question 9

Factor the perfect square trinomial below. $x ^ { 2 } + 18 x + 81$

Accepted Answer

A)  $( x + 18 ) ^ { 2 }$ 
B)  $( x - 18 ) ^ { 2 }$ 
C)  $( x + 9 ) ( x - 9 )$ 
D)  $( x + 9 ) ^ { 2 }$ 
E)  $( x - 9 ) ^ { 2 }$ 
A)  $( x + 18 ) ^ { 2 }$ 
B)  $( x - 18 ) ^ { 2 }$ 
C)  $( x + 9 ) ( x - 9 )$ 
D)  $( x + 9 ) ^ { 2 }$ 
E)  $( x - 9 ) ^ { 2 }$

Question 10

Factor the perfect square trinomial below. $64 x ^ { 2 } + 96 x y + 36 y ^ { 2 }$

Accepted Answer

A)  $( 6 x + 8 y ) ^ { 2 }$ 
B)  $( 8 x + 6 y ) ^ { 2 }$ 
C)  $( 8 x - 6 y ) ^ { 2 }$ 
D)  $( 6 x - 8 y ) ^ { 2 }$ 
E)  $( 6 x - 8 y ) ( 6 x + 8 y )$ 
A)  $( 6 x + 8 y ) ^ { 2 }$ 
B)  $( 8 x + 6 y ) ^ { 2 }$ 
C)  $( 8 x - 6 y ) ^ { 2 }$ 
D)  $( 6 x - 8 y ) ^ { 2 }$ 
E)  $( 6 x - 8 y ) ( 6 x + 8 y )$

Question 11

Factor out the greatest common monomial factor from the polynomial $21 y - 12$ .

Accepted Answer

A)  $12 ( 21 y - 4 )$ 
B)  $21 ( y - 4 )$ 
C)  $3 ( 7 y - 12 )$ 
D)  $3 ( 7 y - 4 )$ 
E) no common factor other than 1 
A)  $12 ( 21 y - 4 )$ 
B)  $21 ( y - 4 )$ 
C)  $3 ( 7 y - 12 )$ 
D)  $3 ( 7 y - 4 )$ 
E) no common factor other than 1

Question 12

Factor the trinomial, if possible. $20 y ^ { 2 } - 3 y - 9$

Accepted Answer

A)  $( 5 y + 3 ) ( 4 y - 3 )$ 
B)  $( 5 y - 3 ) ( 4 y - 3 )$ 
C)  $( 3 y + 5 ) ( 3 y - 4 )$ 
D)  $( 5 y + 3 ) ( 4 y + 3 )$ 
E) The trinomial is prime. 
A)  $( 5 y + 3 ) ( 4 y - 3 )$ 
B)  $( 5 y - 3 ) ( 4 y - 3 )$ 
C)  $( 3 y + 5 ) ( 3 y - 4 )$ 
D)  $( 5 y + 3 ) ( 4 y + 3 )$ 
E) The trinomial is prime.

Question 13

Factor the perfect square trinomial below. $\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }$

Accepted Answer

A)  $\left( \frac { 7 } { 6 } x + \frac { 5 } { 4 } \right) ^ { 2 }$ 
B)  $\left( - \frac { 5 } { 4 } x + \frac { 7 } { 6 } \right) ^ { 2 }$ 
C)  $\left( \frac { 5 } { 4 } x + \frac { 7 } { 6 } \right) ^ { 2 }$ 
D)  $\left( \frac { 5 } { 4 } x - \frac { 7 } { 6 } \right)$ 
E)  $\left( - \frac { 5 } { 4 } x - \frac { 7 } { 6 } \right) ^ { 2 }$ 
A)  $\left( \frac { 7 } { 6 } x + \frac { 5 } { 4 } \right) ^ { 2 }$ 
B)  $\left( - \frac { 5 } { 4 } x + \frac { 7 } { 6 } \right) ^ { 2 }$ 
C)  $\left( \frac { 5 } { 4 } x + \frac { 7 } { 6 } \right) ^ { 2 }$ 
D)  $\left( \frac { 5 } { 4 } x - \frac { 7 } { 6 } \right)$ 
E)  $\left( - \frac { 5 } { 4 } x - \frac { 7 } { 6 } \right) ^ { 2 }$

Question 14

Factor the perfect square trinomial $64 a ^ { 2 } - 112 a + 49$ .

Accepted Answer

A)  $( 8 a + 49 ) ^ { 2 }$ 
B)  $( 8 a - 49 ) ^ { 2 }$ 
C)  $( 8 a - 7 ) ^ { 2 }$ 
D)  $( 64 a + 49 ) ^ { 2 }$ 
E)  $( 8 a + 7 ) ^ { 2 }$ 
A)  $( 8 a + 49 ) ^ { 2 }$ 
B)  $( 8 a - 49 ) ^ { 2 }$ 
C)  $( 8 a - 7 ) ^ { 2 }$ 
D)  $( 64 a + 49 ) ^ { 2 }$ 
E)  $( 8 a + 7 ) ^ { 2 }$

Question 15

Write $9 \times 10 ^ { - 5 }$ in decimal notation.

Accepted Answer

A)  $0.00009$ 
B)  $900,000$ 
C)  $9,000,000$ 
D)  $0.000009$ 
E)  $0.0009$ 
A)  $0.00009$ 
B)  $900,000$ 
C)  $9,000,000$ 
D)  $0.000009$ 
E)  $0.0009$

Question 16

Solve the equation below by factoring. $$x ( x + 7 ) = 8$$

Accepted Answer

A)  $x = - 8$ and $x = 1$ 
B)  $x = - 8$ and $x = - 1$ 
C)  $x = - 1$ and $x = 8$ 
D)  $x = - 7$ and $x = 0$ 
E)  $x = 0$ and $x = 7$ 
A)  $x = - 8$ and $x = 1$ 
B)  $x = - 8$ and $x = - 1$ 
C)  $x = - 1$ and $x = 8$ 
D)  $x = - 7$ and $x = 0$ 
E)  $x = 0$ and $x = 7$

Question 17

The masses of Mercury and the sun are approximately $3.3 \times 10 ^ { 23 }$ kilograms and $1.99 \times 10 ^ { 30 }$ kilograms, respectively. The mass of the sun is approximately how many times that of Mercury?

Accepted Answer

A)  3,030 times 
B)  $6,030,303$ times 
C)  16,470 times 
D)  3,919 times 
E)  84,200 times 
A)  3,030 times 
B)  $6,030,303$ times 
C)  16,470 times 
D)  3,919 times 
E)  84,200 times

Question 18

Factor the expression below completely, if possible $18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }$

Accepted Answer

A)  $3 m n ( m - 2 n ) ( 6 m - 7 n )$ 
B)  $3 m n ( m + 2 n ) ( 6 m + 7 n )$ 
C)  $3 m n ( m - 2 n ) ( 6 m + 7 n )$ 
D)  $3 m n ( m + 2 n ) ( 6 m - 7 n )$ 
E) The expression is prime. 
A)  $3 m n ( m - 2 n ) ( 6 m - 7 n )$ 
B)  $3 m n ( m + 2 n ) ( 6 m + 7 n )$ 
C)  $3 m n ( m - 2 n ) ( 6 m + 7 n )$ 
D)  $3 m n ( m + 2 n ) ( 6 m - 7 n )$ 
E) The expression is prime.

Question 19

Factor the polynomial below by grouping. $z ^ { 4 } - 5 z - 9 z ^ { 3 } + 45$

Accepted Answer

A)  $\left( z ^ { 3 } - 9 \right) ( z - 5 )$ 
B)  $\left( z ^ { 3 } + 5 \right) ( z - 9 )$ 
C)  $\left( z ^ { 3 } + 9 \right) ( z - 5 )$ 
D)  $\left( z ^ { 3 } + 9 \right) ( z + 5 )$ 
E)  $\left( z ^ { 3 } - 5 \right) ( z - 9 )$ 
A)  $\left( z ^ { 3 } - 9 \right) ( z - 5 )$ 
B)  $\left( z ^ { 3 } + 5 \right) ( z - 9 )$ 
C)  $\left( z ^ { 3 } + 9 \right) ( z - 5 )$ 
D)  $\left( z ^ { 3 } + 9 \right) ( z + 5 )$ 
E)  $\left( z ^ { 3 } - 5 \right) ( z - 9 )$

Question 20

Solve the equation below by factoring. $$2 u ^ { 3 } = 15 u ^ { 2 } + 8 u$$

Accepted Answer

A)  $u = \frac { 1 } { 2 }$ , $u = 0$ , and $u = 8$ 
B)  $u = - 8$ and $u = 0$ 
C)  $u = - \frac { 1 } { 2 }$ , $u = 0$ , and $u = 8$ 
D)  $u = - \frac { 1 } { 2 }$ , $u = - 8$ , and $u = 0$ 
E)  $u = \frac { 1 } { 2 }$ , $u = - 8$ , and $u = 0$ 
A)  $u = \frac { 1 } { 2 }$ , $u = 0$ , and $u = 8$ 
B)  $u = - 8$ and $u = 0$ 
C)  $u = - \frac { 1 } { 2 }$ , $u = 0$ , and $u = 8$ 
D)  $u = - \frac { 1 } { 2 }$ , $u = - 8$ , and $u = 0$ 
E)  $u = \frac { 1 } { 2 }$ , $u = - 8$ , and $u = 0$

Solve the equation below by factoring. $x ^ { 2 } - 49 = 0$

The open box with a square base is to be constructed from 1056 square inches of material. The height of the box is 5 inches. Find the dimensions of the base.

Simplify the expression $\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }$ . Assume that neither u nor v is zero.

Solve the equation below by factoring. $x ^ { 2 } - 4 x - 45 = 0$

Evaluate the expression $\left( 9 + 3 ^ { - 4 } \right) ^ { 0 }$ .

Find the difference $\left( 9 x ^ { 2 } + 4 x - 10 \right) - \left( 4 x + 9 x ^ { 2 } - 10 \right)$ .

Simplify the expression $( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 }$ .

Factor the trinomial by grouping, if possible. $10 x ^ { 2 } - 9 x - 9$

Factor the perfect square trinomial below. $x ^ { 2 } + 18 x + 81$

Factor the perfect square trinomial below. $64 x ^ { 2 } + 96 x y + 36 y ^ { 2 }$

Factor out the greatest common monomial factor from the polynomial $21 y - 12$ .

Factor the trinomial, if possible. $20 y ^ { 2 } - 3 y - 9$

Factor the perfect square trinomial below. $\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }$

Factor the perfect square trinomial $64 a ^ { 2 } - 112 a + 49$ .

Write $9 \times 10 ^ { - 5 }$ in decimal notation.

Solve the equation below by factoring. $x ( x + 7 ) = 8$

The masses of Mercury and the sun are approximately $3.3 \times 10 ^ { 23 }$ kilograms and $1.99 \times 10 ^ { 30 }$ kilograms, respectively. The mass of the sun is approximately how many times that of Mercury?

Factor the expression below completely, if possible $18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }$

Factor the polynomial below by grouping. $z ^ { 4 } - 5 z - 9 z ^ { 3 } + 45$

Solve the equation below by factoring. $2 u ^ { 3 } = 15 u ^ { 2 } + 8 u$

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

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Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Polynomials and Factoring

Solve the equation below by factoring. x2−49=0x ^ { 2 } - 49 = 0x2−49=0

The open box with a square base is to be constructed from 1056 square inches of material. The height of the box is 5 inches. Find the dimensions of the base.

Simplify the expression 10(uv2)3(5u)3v4\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }(5u)3v410(uv2)3​ . Assume that neither u nor v is zero.

Solve the equation below by factoring. x2−4x−45=0x ^ { 2 } - 4 x - 45 = 0x2−4x−45=0

Evaluate the expression (9+3−4)0\left( 9 + 3 ^ { - 4 } \right) ^ { 0 }(9+3−4)0 .

Find the difference (9x2+4x−10)−(4x+9x2−10)\left( 9 x ^ { 2 } + 4 x - 10 \right) - \left( 4 x + 9 x ^ { 2 } - 10 \right)(9x2+4x−10)−(4x+9x2−10) .

Simplify the expression (st)8(s6t)2( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 }(st)8(s6t)2 .

Factor the trinomial by grouping, if possible. 10x2−9x−910 x ^ { 2 } - 9 x - 910x2−9x−9

Factor the perfect square trinomial below. x2+18x+81x ^ { 2 } + 18 x + 81x2+18x+81

Factor the perfect square trinomial below. 64x2+96xy+36y264 x ^ { 2 } + 96 x y + 36 y ^ { 2 }64x2+96xy+36y2

Factor out the greatest common monomial factor from the polynomial 21y−1221 y - 1221y−12 .

Factor the trinomial, if possible. 20y2−3y−920 y ^ { 2 } - 3 y - 920y2−3y−9

Factor the perfect square trinomial below. 2516x2+3512x+4936\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }1625​x2+1235​x+3649​

Factor the perfect square trinomial 64a2−112a+4964 a ^ { 2 } - 112 a + 4964a2−112a+49 .

Write 9×10−59 \times 10 ^ { - 5 }9×10−5 in decimal notation.

Solve the equation below by factoring. x(x+7)=8x ( x + 7 ) = 8x(x+7)=8

The masses of Mercury and the sun are approximately 3.3×10233.3 \times 10 ^ { 23 }3.3×1023 kilograms and 1.99×10301.99 \times 10 ^ { 30 }1.99×1030 kilograms, respectively. The mass of the sun is approximately how many times that of Mercury?

Factor the expression below completely, if possible 18m3n−57m2n2+42mn318 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }18m3n−57m2n2+42mn3

Factor the polynomial below by grouping. z4−5z−9z3+45z ^ { 4 } - 5 z - 9 z ^ { 3 } + 45z4−5z−9z3+45

Solve the equation below by factoring. 2u3=15u2+8u2 u ^ { 3 } = 15 u ^ { 2 } + 8 u2u3=15u2+8u

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

Solve the equation below by factoring. $x ^ { 2 } - 49 = 0$

Simplify the expression $\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }$ . Assume that neither u nor v is zero.

Solve the equation below by factoring. $x ^ { 2 } - 4 x - 45 = 0$

Evaluate the expression $\left( 9 + 3 ^ { - 4 } \right) ^ { 0 }$ .

Find the difference $\left( 9 x ^ { 2 } + 4 x - 10 \right) - \left( 4 x + 9 x ^ { 2 } - 10 \right)$ .

Simplify the expression $( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 }$ .

Factor the trinomial by grouping, if possible. $10 x ^ { 2 } - 9 x - 9$

Factor the perfect square trinomial below. $x ^ { 2 } + 18 x + 81$

Factor the perfect square trinomial below. $64 x ^ { 2 } + 96 x y + 36 y ^ { 2 }$

Factor out the greatest common monomial factor from the polynomial $21 y - 12$ .

Factor the trinomial, if possible. $20 y ^ { 2 } - 3 y - 9$

Factor the perfect square trinomial below. $\frac { 25 } { 16 } x ^ { 2 } + \frac { 35 } { 12 } x + \frac { 49 } { 36 }$

Factor the perfect square trinomial $64 a ^ { 2 } - 112 a + 49$ .

Write $9 \times 10 ^ { - 5 }$ in decimal notation.

Solve the equation below by factoring. $x ( x + 7 ) = 8$

The masses of Mercury and the sun are approximately $3.3 \times 10 ^ { 23 }$ kilograms and $1.99 \times 10 ^ { 30 }$ kilograms, respectively. The mass of the sun is approximately how many times that of Mercury?

Factor the expression below completely, if possible $18 m ^ { 3 } n - 57 m ^ { 2 } n ^ { 2 } + 42 m n ^ { 3 }$

Factor the polynomial below by grouping. $z ^ { 4 } - 5 z - 9 z ^ { 3 } + 45$

Solve the equation below by factoring. $2 u ^ { 3 } = 15 u ^ { 2 } + 8 u$