Question 1

Find the GCF of 40, 45, and 50.

Accepted Answer

A) 10 
B) 8 
C) 1 
D) 5 
A) 10 
B) 8 
C) 1 
D) 5

Question 2

Factor the polynomial. $$z ^ { 2 } + 6 z + 9$$

Accepted Answer

A)  $( z - 3 ) ^ { 2 }$ 
B)  $( z + 3 ) ^ { 2 }$ 
C)  $( z + 3 ) ( z - 3 )$ 
D)  $( z + 3 ) ( z + 3 )$ 
E) none of these 
A)  $( z - 3 ) ^ { 2 }$ 
B)  $( z + 3 ) ^ { 2 }$ 
C)  $( z + 3 ) ( z - 3 )$ 
D)  $( z + 3 ) ( z + 3 )$ 
E) none of these

Question 3

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). $$4 x ^ { 2 } - 4 x + 1$$

Accepted Answer

A)  $( 2 x + 1 ) ^ { 2 }$ 
B)  $( 2 x - 2 ) ^ { 2 }$ 
C)  $( 2 x - 1 ) ( 2 x + 1 )$ 
D)  $( 2 x - 1 ) ^ { 2 }$ 
E) prime 
A)  $( 2 x + 1 ) ^ { 2 }$ 
B)  $( 2 x - 2 ) ^ { 2 }$ 
C)  $( 2 x - 1 ) ( 2 x + 1 )$ 
D)  $( 2 x - 1 ) ^ { 2 }$ 
E) prime

Question 4

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 5

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

Accepted Answer

A)  $( x - 9 ) ^ { 2 }$ 
B)  $( x + 8 ) ^ { 2 }$ 
C)  $( x + 18 ) ^ { 2 }$ 
D)  $( x + 9 ) ^ { 2 }$ 
E) none of these 
A)  $( x - 9 ) ^ { 2 }$ 
B)  $( x + 8 ) ^ { 2 }$ 
C)  $( x + 18 ) ^ { 2 }$ 
D)  $( x + 9 ) ^ { 2 }$ 
E) none of these

Question 6

Factor the trinomial. $$y ^ { 2 } + 16 y + 63$$

Accepted Answer

A)  $( y + 7 ) ( y + 9 )$ 
B)  $( y + 7 ) ( y + 5 )$ 
C)  $( y + 7 ) ( y - 5 )$ 
D)  $( y + 7 ) ( y - 7 )$ 
E)  $( y + 7 ) ( y - 9 )$ 
A)  $( y + 7 ) ( y + 9 )$ 
B)  $( y + 7 ) ( y + 5 )$ 
C)  $( y + 7 ) ( y - 5 )$ 
D)  $( y + 7 ) ( y - 7 )$ 
E)  $( y + 7 ) ( y - 9 )$

Question 7

Solve the equation. $x ^ { 3 } + 15 x ^ { 2 } = x ^ { 2 } - 49 x$

Accepted Answer

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

Question 8

Factor the polynomial. $$8 a ^ { 3 } - 27 b ^ { 3 }$$

Accepted Answer

A)  $( 2 a - 3 b ) \left( 2 a ^ { 2 } + 6 a b + 3 b ^ { 2 } \right)$ 
B)  $( 2 a + 3 b ) \left( 2 a ^ { 2 } + 6 a b + 3 b ^ { 2 } \right)$ 
C)  $( a - b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
D)  $( a - b ) \left( 4 a ^ { 2 } + 6 a b - 9 b ^ { 2 } \right)$ 
E)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
A)  $( 2 a - 3 b ) \left( 2 a ^ { 2 } + 6 a b + 3 b ^ { 2 } \right)$ 
B)  $( 2 a + 3 b ) \left( 2 a ^ { 2 } + 6 a b + 3 b ^ { 2 } \right)$ 
C)  $( a - b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$ 
D)  $( a - b ) \left( 4 a ^ { 2 } + 6 a b - 9 b ^ { 2 } \right)$ 
E)  $( 2 a - 3 b ) \left( 4 a ^ { 2 } + 6 a b + 9 b ^ { 2 } \right)$

Question 9

Factor the trinomial completely. $$8 x ^ { 2 } + 4 x - 24$$

Accepted Answer

A) ( x - 2)(8 x - 12) 
B) 8 ( x + 1)( x - 3) 
C) 4 ( x + 2)(2 x - 3) 
D) (4 x + 8)(2 x - 3) 
E) not factorable 
A) ( x - 2)(8 x - 12) 
B) 8 ( x + 1)( x - 3) 
C) 4 ( x + 2)(2 x - 3) 
D) (4 x + 8)(2 x - 3) 
E) not factorable

Question 10

Solve the equation. ( x - 5 )( x + 1 )= 0

Accepted Answer

A) 5, -6 
B) 6, -5 
C) 5, -1 
D) -5, 1 
E) none of these 
A) 5, -6 
B) 6, -5 
C) 5, -1 
D) -5, 1 
E) none of these

Question 11

Factor completely. $$91 x ^ { 3 } y ^ { 4 } - 77 x ^ { 4 } y ^ { 3 }$$

Accepted Answer

A)  $7 x ^ { 3 } y ^ { 3 } ( 13 y - 11 x )$ 
B)  $7 y ^ { 3 } \left( 13 x ^ { 3 } y - 11 x ^ { 4 } \right)$ 
C)  $7 x ^ { 3 } \left( 13 y ^ { 4 } - 11 x y ^ { 3 } \right)$ 
D)  $7 \left( 13 y ^ { 4 } y - 11 x ^ { 4 } \right)$ 
E)  $x ^ { 3 } y ^ { 3 } ( 91 y - 77 x )$ 
A)  $7 x ^ { 3 } y ^ { 3 } ( 13 y - 11 x )$ 
B)  $7 y ^ { 3 } \left( 13 x ^ { 3 } y - 11 x ^ { 4 } \right)$ 
C)  $7 x ^ { 3 } \left( 13 y ^ { 4 } - 11 x y ^ { 3 } \right)$ 
D)  $7 \left( 13 y ^ { 4 } y - 11 x ^ { 4 } \right)$ 
E)  $x ^ { 3 } y ^ { 3 } ( 91 y - 77 x )$

Question 12

A booklet is rectangular and its length is 2 centimeters less than 2 times its width. Its area is 40 square centimeters. Find the dimensions of the booklet.

Accepted Answer

A) 5 cm by 8 cm 
B) 4 cm by 14 cm 
C) 4 cm by 8 cm 
D) 5 cm by 14 cm 
A) 5 cm by 8 cm 
B) 4 cm by 14 cm 
C) 4 cm by 8 cm 
D) 5 cm by 14 cm

Question 13

The x - and y -coordinates of a point in quadrant III are consecutive even integers whose product is 360. Find the coordinates of the point.

Accepted Answer

A) (20, 18) 
B) (-20, -18) 
C) (-24, -22) 
D) (24, 22) 
A) (20, 18) 
B) (-20, -18) 
C) (-24, -22) 
D) (24, 22)

Question 14

Factor the expression. $$- 30 a b c - 30 a c ^ { 2 } + 5 b c + 5 c ^ { 2 }$$

Accepted Answer

A)  $- 5 c ( b - c ) ( 6 a + 1 )$ 
B)  $- 5 c ( b - 1 ) ( 6 a + c )$ 
C)  $- 5 c ( b + c ) ( 6 a - 1 )$ 
D)  $5 c ( b - 1 ) ( 6 a + c )$ 
E)  $- 5 c ( b + 1 ) ( 6 a - c )$ 
A)  $- 5 c ( b - c ) ( 6 a + 1 )$ 
B)  $- 5 c ( b - 1 ) ( 6 a + c )$ 
C)  $- 5 c ( b + c ) ( 6 a - 1 )$ 
D)  $5 c ( b - 1 ) ( 6 a + c )$ 
E)  $- 5 c ( b + 1 ) ( 6 a - c )$

Question 15

The product of two consecutive integers is $1406$ . Find the integers.

Accepted Answer

A)  $25$ , $26$ 
B)  $31$ , $32$ 
C)  $37$ , $38$ 
D)  $43$ , $44$ 
A)  $25$ , $26$ 
B)  $31$ , $32$ 
C)  $37$ , $38$ 
D)  $43$ , $44$

Question 16

Factor the polynomial. $$9 z ^ { 2 } - 78 z + 169$$

Accepted Answer

A)  $3 ( z + 13 ) ^ { 2 }$ 
B)  $( 3 z + 13 ) ^ { 2 }$ 
C)  $3 ( 13 - z ) ^ { 2 }$ 
D)  $( 3 z - 13 ) ^ { 2 }$ 
E)  $3 ( z - 13 ) ^ { 2 }$ 
A)  $3 ( z + 13 ) ^ { 2 }$ 
B)  $( 3 z + 13 ) ^ { 2 }$ 
C)  $3 ( 13 - z ) ^ { 2 }$ 
D)  $( 3 z - 13 ) ^ { 2 }$ 
E)  $3 ( z - 13 ) ^ { 2 }$

Question 17

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 9 x + 1 = 1$

Accepted Answer

A)  $0$ 
B)  $\pm9$ 
C)  $0 , - 9$ 
D)  $0,9$ 
E)  $9$ 
A)  $0$ 
B)  $\pm9$ 
C)  $0 , - 9$ 
D)  $0,9$ 
E)  $9$

Question 18

Factor the following perfect square trinomial. $$a ^ { 2 } + 6 a + 9$$

Accepted Answer

A)  $( a - 3 ) ^ { 2 }$ 
B)  $( a + 2 ) ^ { 2 }$ 
C)  $( a + 6 ) ^ { 2 }$ 
D)  $( a + 3 ) ^ { 2 }$ 
E) none of these 
A)  $( a - 3 ) ^ { 2 }$ 
B)  $( a + 2 ) ^ { 2 }$ 
C)  $( a + 6 ) ^ { 2 }$ 
D)  $( a + 3 ) ^ { 2 }$ 
E) none of these

Question 19

Factor the trinomial. Factor out the GCF first. $$24 x ^ { 6 } - 10 x ^ { 4 } - 21 x ^ { 2 }$$

Accepted Answer

A)  $2 x ^ { 2 } \left( 6 x ^ { 2 } - 7 \right) \left( x ^ { 2 } + 3 \right)$ 
B)  $\left( 6 x ^ { 2 } - 7 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
C)  $x ^ { 2 } \left( 6 x ^ { 2 } - 8 \right) \left( 4 x ^ { 2 } - 3 \right)$ 
D)  $x ^ { 2 } \left( 6 x ^ { 2 } - 5 \right) \left( 4 x ^ { 2 } - 3 \right)$ 
E)  $x ^ { 2 } \left( 6 x ^ { 2 } - 7 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
A)  $2 x ^ { 2 } \left( 6 x ^ { 2 } - 7 \right) \left( x ^ { 2 } + 3 \right)$ 
B)  $\left( 6 x ^ { 2 } - 7 \right) \left( 4 x ^ { 2 } + 3 \right)$ 
C)  $x ^ { 2 } \left( 6 x ^ { 2 } - 8 \right) \left( 4 x ^ { 2 } - 3 \right)$ 
D)  $x ^ { 2 } \left( 6 x ^ { 2 } - 5 \right) \left( 4 x ^ { 2 } - 3 \right)$ 
E)  $x ^ { 2 } \left( 6 x ^ { 2 } - 7 \right) \left( 4 x ^ { 2 } + 3 \right)$

Question 20

Give the name for this type of equation. 6 x  2 + 9 x + 8 = 0

Accepted Answer

A) cubic 
B) quadratic 
C) linear 
D) true 
E) none of these 
A) cubic 
B) quadratic 
C) linear 
D) true 
E) none of these

Find the GCF of 40, 45, and 50.

Factor the polynomial. $z ^ { 2 } + 6 z + 9$

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). $4 x ^ { 2 } - 4 x + 1$

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

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

Factor the trinomial. $y ^ { 2 } + 16 y + 63$

Solve the equation. $x ^ { 3 } + 15 x ^ { 2 } = x ^ { 2 } - 49 x$

Factor the polynomial. $8 a ^ { 3 } - 27 b ^ { 3 }$

Factor the trinomial completely. $8 x ^ { 2 } + 4 x - 24$

Solve the equation. ( x - 5 )( x + 1 )= 0

Factor completely. $91 x ^ { 3 } y ^ { 4 } - 77 x ^ { 4 } y ^ { 3 }$

A booklet is rectangular and its length is 2 centimeters less than 2 times its width. Its area is 40 square centimeters. Find the dimensions of the booklet.

The x - and y -coordinates of a point in quadrant III are consecutive even integers whose product is 360. Find the coordinates of the point.

Factor the expression. $- 30 a b c - 30 a c ^ { 2 } + 5 b c + 5 c ^ { 2 }$

The product of two consecutive integers is $1406$ . Find the integers.

Factor the polynomial. $9 z ^ { 2 } - 78 z + 169$

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 9 x + 1 = 1$

Factor the following perfect square trinomial. $a ^ { 2 } + 6 a + 9$

Factor the trinomial. Factor out the GCF first. $24 x ^ { 6 } - 10 x ^ { 4 } - 21 x ^ { 2 }$

Give the name for this type of equation. 6 x ²+ 9 x + 8 = 0

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 6: Factoring and Quadratic Equations

Find the GCF of 40, 45, and 50.

Factor the polynomial. z2+6z+9z ^ { 2 } + 6 z + 9z2+6z+9

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). 4x2−4x+14 x ^ { 2 } - 4 x + 14x2−4x+1

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

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

Factor the trinomial. y2+16y+63y ^ { 2 } + 16 y + 63y2+16y+63

Solve the equation. x3+15x2=x2−49xx ^ { 3 } + 15 x ^ { 2 } = x ^ { 2 } - 49 xx3+15x2=x2−49x

Factor the polynomial. 8a3−27b38 a ^ { 3 } - 27 b ^ { 3 }8a3−27b3

Factor the trinomial completely. 8x2+4x−248 x ^ { 2 } + 4 x - 248x2+4x−24

Solve the equation. ( x - 5 )( x + 1 )= 0

Factor completely. 91x3y4−77x4y391 x ^ { 3 } y ^ { 4 } - 77 x ^ { 4 } y ^ { 3 }91x3y4−77x4y3

A booklet is rectangular and its length is 2 centimeters less than 2 times its width. Its area is 40 square centimeters. Find the dimensions of the booklet.

The x - and y -coordinates of a point in quadrant III are consecutive even integers whose product is 360. Find the coordinates of the point.

Factor the expression. −30abc−30ac2+5bc+5c2- 30 a b c - 30 a c ^ { 2 } + 5 b c + 5 c ^ { 2 }−30abc−30ac2+5bc+5c2

The product of two consecutive integers is 140614061406 . Find the integers.

Factor the polynomial. 9z2−78z+1699 z ^ { 2 } - 78 z + 1699z2−78z+169

Factor the trinomial square and use the square root method to solve the equation. x2−9x+1=1x ^ { 2 } - 9 x + 1 = 1x2−9x+1=1

Factor the following perfect square trinomial. a2+6a+9a ^ { 2 } + 6 a + 9a2+6a+9

Factor the trinomial. Factor out the GCF first. 24x6−10x4−21x224 x ^ { 6 } - 10 x ^ { 4 } - 21 x ^ { 2 }24x6−10x4−21x2

Give the name for this type of equation. 6 x 2 + 9 x + 8 = 0

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Exponents and Polynomials

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Factor the polynomial. $z ^ { 2 } + 6 z + 9$

Factor the expression, if possible. Factor out any GCF first (including -1 if the leading coefficient is negative). $4 x ^ { 2 } - 4 x + 1$

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

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

Factor the trinomial. $y ^ { 2 } + 16 y + 63$

Solve the equation. $x ^ { 3 } + 15 x ^ { 2 } = x ^ { 2 } - 49 x$

Factor the polynomial. $8 a ^ { 3 } - 27 b ^ { 3 }$

Factor the trinomial completely. $8 x ^ { 2 } + 4 x - 24$

Factor completely. $91 x ^ { 3 } y ^ { 4 } - 77 x ^ { 4 } y ^ { 3 }$

Factor the expression. $- 30 a b c - 30 a c ^ { 2 } + 5 b c + 5 c ^ { 2 }$

The product of two consecutive integers is $1406$ . Find the integers.

Factor the polynomial. $9 z ^ { 2 } - 78 z + 169$

Factor the trinomial square and use the square root method to solve the equation. $x ^ { 2 } - 9 x + 1 = 1$

Factor the following perfect square trinomial. $a ^ { 2 } + 6 a + 9$

Factor the trinomial. Factor out the GCF first. $24 x ^ { 6 } - 10 x ^ { 4 } - 21 x ^ { 2 }$

Give the name for this type of equation. 6 x ²+ 9 x + 8 = 0