Question 1

Find the quotient. $$\frac { 15 x ^ { 5 } y ^ { 5 } } { 3 x y ^ { 3 } }$$

Accepted Answer

A)  $x ^ { 5 } y ^ { 2 }$ 
B)  $5 x ^ { 5 } y ^ { 4 }$ 
C)  $5 x ^ { 5 } y ^ { 2 }$ 
D)  $5 x ^ { 4 } y ^ { 2 }$ 
E)  $5 x ^ { 4 } y ^ { 4 }$ 
A)  $x ^ { 5 } y ^ { 2 }$ 
B)  $5 x ^ { 5 } y ^ { 4 }$ 
C)  $5 x ^ { 5 } y ^ { 2 }$ 
D)  $5 x ^ { 4 } y ^ { 2 }$ 
E)  $5 x ^ { 4 } y ^ { 4 }$ D

Question 2

Factor the expression. $$33 a ^ { 2 } b ^ { 2 } ( 7 x - 2 y ) - 6 a b ( 7 x - 2 y )$$

Accepted Answer

A)  $3 a b ( 7 x - 2 y ) ( 11 a b - 2 )$ 
B)  $3 a b ( 7 x - 2 y ) ( 11 a b - 2 )$. 
C)  $3 a b ( 7 x + 2 y ) ( 11 a b - 2 )$ 
D)  $3 a b ( 7 x - 2 y ) ( 11 a b - 2 a b )$ 
E)  $3 a b ( 7 x - 2 y ) ( 11 a b + 2 a b )$. 
A)  $3 a b ( 7 x - 2 y ) ( 11 a b - 2 )$ 
B)  $3 a b ( 7 x - 2 y ) ( 11 a b - 2 )$. 
C)  $3 a b ( 7 x + 2 y ) ( 11 a b - 2 )$ 
D)  $3 a b ( 7 x - 2 y ) ( 11 a b - 2 a b )$ 
E)  $3 a b ( 7 x - 2 y ) ( 11 a b + 2 a b )$. A

Question 3

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Accepted Answer

A)  $\frac { ( - 10 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 10 - \sqrt { 61 } ) } { 7 }$ 
B)  $\frac { ( - 6 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 6 - \sqrt { 61 } ) } { 7 }$ 
C)  $\frac { ( - 7 + \sqrt { 61 } ) } { 6 }$ , $\frac { ( - 7 - \sqrt { 61 } ) } { 6 }$ 
D)  $\frac { ( - 8 \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 8 - \sqrt { 61 } ) } { 7 }$ 
A)  $\frac { ( - 10 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 10 - \sqrt { 61 } ) } { 7 }$ 
B)  $\frac { ( - 6 + \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 6 - \sqrt { 61 } ) } { 7 }$ 
C)  $\frac { ( - 7 + \sqrt { 61 } ) } { 6 }$ , $\frac { ( - 7 - \sqrt { 61 } ) } { 6 }$ 
D)  $\frac { ( - 8 \sqrt { 61 } ) } { 7 }$ , $\frac { ( - 8 - \sqrt { 61 } ) } { 7 }$ C

Question 4

Find the product. $$\left( a ^ { 4 n } + t ^ { 4 n } \right) \left( a ^ { 4 n } - t ^ { 4 n } \right)$$

Accepted Answer

A)  $a ^ { 8 n } - t ^ { 4 n }$ 
B)  $a ^ { 8 n } + t ^ { 8 n }$ 
C)  $a ^ { 4 n } - t ^ { 8 n }$ 
D)  $t ^ { 8 n } - a ^ { 8 n }$ 
E)  $a ^ { 8 n } - t ^ { 8 n }$ 
A)  $a ^ { 8 n } - t ^ { 4 n }$ 
B)  $a ^ { 8 n } + t ^ { 8 n }$ 
C)  $a ^ { 4 n } - t ^ { 8 n }$ 
D)  $t ^ { 8 n } - a ^ { 8 n }$ 
E)  $a ^ { 8 n } - t ^ { 8 n }$

Question 5

Completely factor the expression. $$3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$$

Accepted Answer

A)  $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$ 
B)  $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$ 
C)  $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$ 
D)  $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$ 
E) prime 
A)  $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$ 
B)  $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$ 
C)  $3 ( x - 2 ) ^ { 2 } \left( a ^ { 2 } + 2 b ^ { 2 } \right)$ 
D)  $3 ( x + 2 ) ^ { 2 } \left( a ^ { 2 } - 2 b ^ { 2 } \right)$ 
E) prime

Question 6

Find the product. $( 5 s + z ) ^ { 2 }$

Accepted Answer

A)  $25 s ^ { 2 } + 10 s z + z ^ { 2 }$ 
B)  $23 s ^ { 2 } + 14 s z + z ^ { 2 }$ 
C)  $29 s ^ { 2 } + 16 s z + z ^ { 2 }$ 
D)  $32 s ^ { 2 } + 13 s z + z ^ { 2 }$ 
E)  $26 s ^ { 2 } + 15 s z + z ^ { 2 }$ 
A)  $25 s ^ { 2 } + 10 s z + z ^ { 2 }$ 
B)  $23 s ^ { 2 } + 14 s z + z ^ { 2 }$ 
C)  $29 s ^ { 2 } + 16 s z + z ^ { 2 }$ 
D)  $32 s ^ { 2 } + 13 s z + z ^ { 2 }$ 
E)  $26 s ^ { 2 } + 15 s z + z ^ { 2 }$

Question 7

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 5 x + 9 = 9$

Accepted Answer

A)  $0$ 
B)  $\pm 5$ 
C)  $0 , - 5$ 
D)  $0,5$ 
E)  $5$ 
A)  $0$ 
B)  $\pm 5$ 
C)  $0 , - 5$ 
D)  $0,5$ 
E)  $5$

Question 8

Factor completely. $42 x ^ { 3 } y ^ { 4 } - 30 x ^ { 4 } y ^ { 3 }$

Accepted Answer

A)  $6 x ^ { 3 } y ^ { 3 } ( 7 y - 5 x )$ 
B)  $6 y ^ { 3 } \left( 7 x ^ { 3 } y - 5 x ^ { 4 } \right)$ 
C)  $6 x ^ { 3 } \left( 7 y ^ { 4 } - 5 x y ^ { 3 } \right)$ 
D)  $6 \left( 7 y ^ { 4 } y - 5 x ^ { 4 } \right)$ 
E)  $x ^ { 3 } y ^ { 3 } ( 42 y - 30 x )$ 
A)  $6 x ^ { 3 } y ^ { 3 } ( 7 y - 5 x )$ 
B)  $6 y ^ { 3 } \left( 7 x ^ { 3 } y - 5 x ^ { 4 } \right)$ 
C)  $6 x ^ { 3 } \left( 7 y ^ { 4 } - 5 x y ^ { 3 } \right)$ 
D)  $6 \left( 7 y ^ { 4 } y - 5 x ^ { 4 } \right)$ 
E)  $x ^ { 3 } y ^ { 3 } ( 42 y - 30 x )$

Question 9

Factor by grouping. $$a x ^ { 2 } - x ^ { 2 } + 7 a - 7$$

Accepted Answer

A)  $x ^ { 2 } + 7 ( a - 1 )$ 
B)  $a x ^ { 2 } + 7 a - \left( x ^ { 2 } + 7 \right)$ 
C)  $\left( x ^ { 2 } + 7 \right) ( a - 1 )$ 
D)  $\left( x ^ { 2 } - 7 \right) a + x ^ { 2 } + 7$ 
E)  $\left( x ^ { 2 } + 7 \right) a - x ^ { 2 } - 7$ 
A)  $x ^ { 2 } + 7 ( a - 1 )$ 
B)  $a x ^ { 2 } + 7 a - \left( x ^ { 2 } + 7 \right)$ 
C)  $\left( x ^ { 2 } + 7 \right) ( a - 1 )$ 
D)  $\left( x ^ { 2 } - 7 \right) a + x ^ { 2 } + 7$ 
E)  $\left( x ^ { 2 } + 7 \right) a - x ^ { 2 } - 7$

Question 10

Raise the monomial to the indicated power. $- ( 5 a b ) ^ { 3 }$

Accepted Answer

A)  $- 125 a ^ { 4 } b ^ { 4 }$ 
B)  $- 15 a ^ { 4 } b ^ { 4 }$ 
C)  $15 a ^ { 3 } b ^ { 3 }$ 
D)  $- 125 a ^ { 3 } b ^ { 3 }$ 
E)  $125 a ^ { 4 } b ^ { 4 }$ 
A)  $- 125 a ^ { 4 } b ^ { 4 }$ 
B)  $- 15 a ^ { 4 } b ^ { 4 }$ 
C)  $15 a ^ { 3 } b ^ { 3 }$ 
D)  $- 125 a ^ { 3 } b ^ { 3 }$ 
E)  $125 a ^ { 4 } b ^ { 4 }$

Question 11

Find two integers whose product is 405 such that one of the integers is three less than twice the other integer.

Accepted Answer

A) 16, 26 
B) 14, 26 
C) 15, 27 
D) 16, 28 
E) 14, 28 
A) 16, 26 
B) 14, 26 
C) 15, 27 
D) 16, 28 
E) 14, 28

Question 12

Factor the expression. $( a - n ) c + ( a - n ) d$

Accepted Answer

A)  $( d - n ) ( c + a )$ 
B)  $( a - d ) ( c + n )$ 
C)  $c ( a - d ) + d$ 
D)  $( a - n ) ( c + d )$ 
E)  $( n - a ) ( c + d )$ 
A)  $( d - n ) ( c + a )$ 
B)  $( a - d ) ( c + n )$ 
C)  $c ( a - d ) + d$ 
D)  $( a - n ) ( c + d )$ 
E)  $( n - a ) ( c + d )$

Question 13

Factor completely the polynomial. Indicate any that are not factorable using integers. 24 x  2 + 58 x + 35

Accepted Answer

A) (4 x - 5)(6 x - 7) 
B) (4 x + 5)(6 x - 7) 
C) (4 x - 5)(6 x + 7) 
D) (4 x + 5)(6 x + 7) 
E) not factorable 
A) (4 x - 5)(6 x - 7) 
B) (4 x + 5)(6 x - 7) 
C) (4 x - 5)(6 x + 7) 
D) (4 x + 5)(6 x + 7) 
E) not factorable

Question 14

Find the product. $$\left( y a ^ { 3 } \right) \left( 2 y ^ { 5 } a ^ { 6 } \right) \left( 3 y ^ { 2 } a \right)$$

Accepted Answer

A)  $5 y ^ { 8 } a ^ { 10 }$ 
B)  $6 y ^ { 8 } a ^ { 10 }$ 
C)  $6 y ^ { 12 } a ^ { 24 }$ 
D)  $6 y ^ { 4 } a ^ { 2 }$ 
E) none of these 
A)  $5 y ^ { 8 } a ^ { 10 }$ 
B)  $6 y ^ { 8 } a ^ { 10 }$ 
C)  $6 y ^ { 12 } a ^ { 24 }$ 
D)  $6 y ^ { 4 } a ^ { 2 }$ 
E) none of these

Question 15

Factor completely the polynomial. Indicate any that are not factorable using integers. a  2 - 4 a + 21

Accepted Answer

A) ( a - 3)( a + 7) 
B) ( a + 3)( a - 7) 
C) ( a - 3)( a - 7) 
D) ( a + 3)( a + 7) 
E) not factorable 
A) ( a - 3)( a + 7) 
B) ( a + 3)( a - 7) 
C) ( a - 3)( a - 7) 
D) ( a + 3)( a + 7) 
E) not factorable

Question 16

Factor completely the polynomial. Indicate any that are not factorable using integers. x  2 - 10 x + 21

Accepted Answer

A) ( x + 3)( x + 7) 
B) ( x + 3)( x - 7) 
C) ( x - 3)( x - 7) 
D) ( x - 3)( x + 7) 
E) not factorable 
A) ( x + 3)( x + 7) 
B) ( x + 3)( x - 7) 
C) ( x - 3)( x - 7) 
D) ( x - 3)( x + 7) 
E) not factorable

Question 17

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9 y ^ { 2 }$

Accepted Answer

A) ( x - 9 y )( x + 9 y ) 
B) ( x + 3 y )( x + 9 y ) 
C) ( x - 3 y )( x + 3 y ) 
D) ( x - 3 y )( x - 9 y ) 
E) none of these 
A) ( x - 9 y )( x + 9 y ) 
B) ( x + 3 y )( x + 9 y ) 
C) ( x - 3 y )( x + 3 y ) 
D) ( x - 3 y )( x - 9 y ) 
E) none of these

Question 18

Find the product. $\left( 4 x ^ { 3 } \right) \left( 3 x ^ { 5 } \right)$

Accepted Answer

A)  $12 x ^ { 8 }$ 
B)  $12 x ^ { 15 }$ 
C)  $7 x ^ { 8 }$ 
D)  $7 x ^ { 15 }$ 
E) none of these 
A)  $12 x ^ { 8 }$ 
B)  $12 x ^ { 15 }$ 
C)  $7 x ^ { 8 }$ 
D)  $7 x ^ { 15 }$ 
E) none of these

Question 19

Simplify the expression. $$\left( 20 z ^ { 2 } + 10 z + 6 \right) + \left( 9 z ^ { 2 } + 9 z + 1 \right)$$

Accepted Answer

A)  $29 z ^ { 2 } + 10 z + 7$ 
B)  $29 z ^ { 2 } + 19 z + 7$ 
C)  $29 z ^ { 2 } + 19 z$ 
D)  $20 z ^ { 2 } + 19 z + 7$ 
E) none of these 
A)  $29 z ^ { 2 } + 10 z + 7$ 
B)  $29 z ^ { 2 } + 19 z + 7$ 
C)  $29 z ^ { 2 } + 19 z$ 
D)  $20 z ^ { 2 } + 19 z + 7$ 
E) none of these

Question 20

Factor completely the polynomial. Indicate any that are not factorable using integers. x  2 + 10 xy + 24 y  2

Accepted Answer

A) ( x + 4 y )( x - 6 y ) 
B) ( x + 4 y )( x + 6 y ) 
C) ( x - 4 y )( x + 6 y ) 
D) ( x - 4 y )( x - 6 y ) 
E) not factorable 
A) ( x + 4 y )( x - 6 y ) 
B) ( x + 4 y )( x + 6 y ) 
C) ( x - 4 y )( x + 6 y ) 
D) ( x - 4 y )( x - 6 y ) 
E) not factorable

Find the quotient. $\frac { 15 x ^ { 5 } y ^ { 5 } } { 3 x y ^ { 3 } }$

Factor the expression. $33 a ^ { 2 } b ^ { 2 } ( 7 x - 2 y ) - 6 a b ( 7 x - 2 y )$

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Find the product. $\left( a ^ { 4 n } + t ^ { 4 n } \right) \left( a ^ { 4 n } - t ^ { 4 n } \right)$

Completely factor the expression. $3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$

Find the product. $( 5 s + z ) ^ { 2 }$

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 5 x + 9 = 9$

Factor completely. $42 x ^ { 3 } y ^ { 4 } - 30 x ^ { 4 } y ^ { 3 }$

Factor by grouping. $a x ^ { 2 } - x ^ { 2 } + 7 a - 7$

Raise the monomial to the indicated power. $- ( 5 a b ) ^ { 3 }$

Find two integers whose product is 405 such that one of the integers is three less than twice the other integer.

Factor the expression. $( a - n ) c + ( a - n ) d$

Factor completely the polynomial. Indicate any that are not factorable using integers. 24 x ² + 58 x + 35

Find the product. $\left( y a ^ { 3 } \right) \left( 2 y ^ { 5 } a ^ { 6 } \right) \left( 3 y ^ { 2 } a \right)$

Factor completely the polynomial. Indicate any that are not factorable using integers. a ² - 4 a + 21

Factor completely the polynomial. Indicate any that are not factorable using integers. x ² - 10 x + 21

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9 y ^ { 2 }$

Find the product. $\left( 4 x ^ { 3 } \right) \left( 3 x ^ { 5 } \right)$

Simplify the expression. $\left( 20 z ^ { 2 } + 10 z + 6 \right) + \left( 9 z ^ { 2 } + 9 z + 1 \right)$

Factor completely the polynomial. Indicate any that are not factorable using integers. x ² + 10 xy + 24 y ²

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 3: Polynomials

Find the quotient. 15x5y53xy3\frac { 15 x ^ { 5 } y ^ { 5 } } { 3 x y ^ { 3 } }3xy315x5y5​

Factor the expression. 33a2b2(7x−2y)−6ab(7x−2y)33 a ^ { 2 } b ^ { 2 } ( 7 x - 2 y ) - 6 a b ( 7 x - 2 y )33a2b2(7x−2y)−6ab(7x−2y)

Factor the trinomial square and use the square root method to solve the equation. 3x2+7x+1=23 x ^ { 2 } + 7 x + 1 = 23x2+7x+1=2

Find the product. (a4n+t4n)(a4n−t4n)\left( a ^ { 4 n } + t ^ { 4 n } \right) \left( a ^ { 4 n } - t ^ { 4 n } \right)(a4n+t4n)(a4n−t4n)

Completely factor the expression. 3a2x2+12a2x+12a2−6b2x2−24b2x−24b23 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }3a2x2+12a2x+12a2−6b2x2−24b2x−24b2

Find the product. (5s+z)2( 5 s + z ) ^ { 2 }(5s+z)2

Factor the trinomial square and use the square root method to solve the equation. x2−5x+9=9x ^ { 2 } - 5 x + 9 = 9x2−5x+9=9

Factor completely. 42x3y4−30x4y342 x ^ { 3 } y ^ { 4 } - 30 x ^ { 4 } y ^ { 3 }42x3y4−30x4y3

Factor by grouping. ax2−x2+7a−7a x ^ { 2 } - x ^ { 2 } + 7 a - 7ax2−x2+7a−7

Raise the monomial to the indicated power. −(5ab)3- ( 5 a b ) ^ { 3 }−(5ab)3

Find two integers whose product is 405 such that one of the integers is three less than twice the other integer.

Factor the expression. (a−n)c+(a−n)d( a - n ) c + ( a - n ) d(a−n)c+(a−n)d

Factor completely the polynomial. Indicate any that are not factorable using integers. 24 x 2 + 58 x + 35

Find the product. (ya3)(2y5a6)(3y2a)\left( y a ^ { 3 } \right) \left( 2 y ^ { 5 } a ^ { 6 } \right) \left( 3 y ^ { 2 } a \right)(ya3)(2y5a6)(3y2a)

Factor completely the polynomial. Indicate any that are not factorable using integers. a 2 - 4 a + 21

Factor completely the polynomial. Indicate any that are not factorable using integers. x 2 - 10 x + 21

Use the difference of squares pattern to factor the polynomial. x2−9y2x ^ { 2 } - 9 y ^ { 2 }x2−9y2

Find the product. (4x3)(3x5)\left( 4 x ^ { 3 } \right) \left( 3 x ^ { 5 } \right)(4x3)(3x5)

Simplify the expression. (20z2+10z+6)+(9z2+9z+1)\left( 20 z ^ { 2 } + 10 z + 6 \right) + \left( 9 z ^ { 2 } + 9 z + 1 \right)(20z2+10z+6)+(9z2+9z+1)

Factor completely the polynomial. Indicate any that are not factorable using integers. x 2 + 10 xy + 24 y 2

Basic Concepts and Properties

Equations, Inequalities, and Problem Solving

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Find the quotient. $\frac { 15 x ^ { 5 } y ^ { 5 } } { 3 x y ^ { 3 } }$

Factor the expression. $33 a ^ { 2 } b ^ { 2 } ( 7 x - 2 y ) - 6 a b ( 7 x - 2 y )$

Factor the trinomial square and use the square root method to solve the equation. $3 x ^ { 2 } + 7 x + 1 = 2$

Find the product. $\left( a ^ { 4 n } + t ^ { 4 n } \right) \left( a ^ { 4 n } - t ^ { 4 n } \right)$

Completely factor the expression. $3 a ^ { 2 } x ^ { 2 } + 12 a ^ { 2 } x + 12 a ^ { 2 } - 6 b ^ { 2 } x ^ { 2 } - 24 b ^ { 2 } x - 24 b ^ { 2 }$

Find the product. $( 5 s + z ) ^ { 2 }$

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 5 x + 9 = 9$

Factor completely. $42 x ^ { 3 } y ^ { 4 } - 30 x ^ { 4 } y ^ { 3 }$

Factor by grouping. $a x ^ { 2 } - x ^ { 2 } + 7 a - 7$

Raise the monomial to the indicated power. $- ( 5 a b ) ^ { 3 }$

Factor the expression. $( a - n ) c + ( a - n ) d$

Factor completely the polynomial. Indicate any that are not factorable using integers. 24 x ² + 58 x + 35

Find the product. $\left( y a ^ { 3 } \right) \left( 2 y ^ { 5 } a ^ { 6 } \right) \left( 3 y ^ { 2 } a \right)$

Factor completely the polynomial. Indicate any that are not factorable using integers. a ² - 4 a + 21

Factor completely the polynomial. Indicate any that are not factorable using integers. x ² - 10 x + 21

Use the difference of squares pattern to factor the polynomial. $x ^ { 2 } - 9 y ^ { 2 }$

Find the product. $\left( 4 x ^ { 3 } \right) \left( 3 x ^ { 5 } \right)$

Simplify the expression. $\left( 20 z ^ { 2 } + 10 z + 6 \right) + \left( 9 z ^ { 2 } + 9 z + 1 \right)$

Factor completely the polynomial. Indicate any that are not factorable using integers. x ² + 10 xy + 24 y ²