Question 1

Factor out the GCF from the polynomial.
-$16 m ^ { 9 } + 8 m ^ { 6 } + 10 m ^ { 3 }$

Accepted Answer

A)  $2 \left( 8 m ^ { 9 } + 4 m ^ { 6 } + 5 m ^ { 3 } \right)$ 
B)  $m ^ { 3 } \left( 16 m ^ { 6 } + 8 m ^ { 3 } + 10 \right)$ 
C)  $2 m ^ { 3 } \left( 8 m ^ { 6 } + 4 m ^ { 3 } + 5 \right)$ 
D)  no common factor 
A)  $2 \left( 8 m ^ { 9 } + 4 m ^ { 6 } + 5 m ^ { 3 } \right)$ 
B)  $m ^ { 3 } \left( 16 m ^ { 6 } + 8 m ^ { 3 } + 10 \right)$ 
C)  $2 m ^ { 3 } \left( 8 m ^ { 6 } + 4 m ^ { 3 } + 5 \right)$ 
D)  no common factor

Question 2

Factor the perfect square trinomial completely.
-$49 x ^ { 2 } - 42 x y + 9 y ^ { 2 }$

Accepted Answer

A)  $( 7 x + 3 y ) ^ { 2 }$ 
B)  $( 7 x - 3 y ) ^ { 2 }$ 
C)  $( 49 x + y ) ( x + 9 y )$ 
D)  $( 7 x - 3 y ) ( 7 x + 3 y )$ 
A)  $( 7 x + 3 y ) ^ { 2 }$ 
B)  $( 7 x - 3 y ) ^ { 2 }$ 
C)  $( 49 x + y ) ( x + 9 y )$ 
D)  $( 7 x - 3 y ) ( 7 x + 3 y )$

Question 3

Solve the equation.
-$x ^ { 2 } - 49 = 48 x$

Accepted Answer

A)  $- 7 , - 7$ 
B)  $1 , - 49$ 
C)  $- 7,7$ 
D)  $- 1,49$ 
A)  $- 7 , - 7$ 
B)  $1 , - 49$ 
C)  $- 7,7$ 
D)  $- 1,49$

Question 4

Solve.
-Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Accepted Answer

A)  $17 \mathrm {~m}$ 
B)  $10 \mathrm {~m}$ 
C)  $18 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$ 
A)  $17 \mathrm {~m}$ 
B)  $10 \mathrm {~m}$ 
C)  $18 \mathrm {~m}$ 
D)  $9 \mathrm {~m}$

Question 5

Factor the four-term polynomial by grouping.
-$24 a ^ { 3 } + 30 a ^ { 2 } b - 20 a b ^ { 2 } - 25 b ^ { 3 }$

Accepted Answer

A)  $\left( 6 a ^ { 2 } - 5 b \right) ( 4 a + 5 b )$ 
B)  $\left( 24 a ^ { 2 } - 5 b ^ { 2 } \right) ( a + 5 b )$ 
C)  $\left( 6 a ^ { 2 } - 5 b ^ { 2 } \right) ( 4 a + 5 b )$ 
D)  $\left( 6 a ^ { 2 } + 5 b ^ { 2 } \right) ( 4 a - 5 b )$ 
A)  $\left( 6 a ^ { 2 } - 5 b \right) ( 4 a + 5 b )$ 
B)  $\left( 24 a ^ { 2 } - 5 b ^ { 2 } \right) ( a + 5 b )$ 
C)  $\left( 6 a ^ { 2 } - 5 b ^ { 2 } \right) ( 4 a + 5 b )$ 
D)  $\left( 6 a ^ { 2 } + 5 b ^ { 2 } \right) ( 4 a - 5 b )$

Question 6

Factor the binomial completely.
-$x ^ { 2 } - \frac { 16 } { 49 }$

Accepted Answer

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

Question 7

Factor the four-term polynomial by grouping.
-$x ^ { 3 } + 3 x ^ { 2 } + x + 3$

Accepted Answer

A)  $\left( x ^ { 2 } + 3 \right) ( x + 1 )$ 
B)  $\left( 3 x ^ { 2 } + 3 \right) ( x + 1 )$ 
C)  $\left( x ^ { 2 } + 1 \right) ( x + 3 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( 3 x + 3 )$ 
A)  $\left( x ^ { 2 } + 3 \right) ( x + 1 )$ 
B)  $\left( 3 x ^ { 2 } + 3 \right) ( x + 1 )$ 
C)  $\left( x ^ { 2 } + 1 \right) ( x + 3 )$ 
D)  $\left( x ^ { 2 } + 1 \right) ( 3 x + 3 )$

Question 8

Factor the binomial completely.
-$x ^ { 4 } - 81$

Accepted Answer

A)  $\left( x ^ { 2 } - 9 \right) \left( x ^ { 2 } - 9 \right)$ 
B)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } + 9 \right)$ 
C)  $\left( x ^ { 2 } + 9 \right) ( x + 3 ) ( x - 3 )$ 
D)  prime 
A)  $\left( x ^ { 2 } - 9 \right) \left( x ^ { 2 } - 9 \right)$ 
B)  $\left( x ^ { 2 } + 9 \right) \left( x ^ { 2 } + 9 \right)$ 
C)  $\left( x ^ { 2 } + 9 \right) ( x + 3 ) ( x - 3 )$ 
D)  prime

Question 9

Factor the sum or difference of two cubes.
-$54 x ^ { 3 } - 128 x ^ { 6 }$

Accepted Answer

A)  $2 x ^ { 3 } ( 3 - 4 x ) \left( 9 + 12 x + 16 x ^ { 2 } \right)$ 
B)  $2 \left( 3 x + 4 x ^ { 2 } \right) \left( 9 x ^ { 2 } - 12 x ^ { 3 } + 16 x ^ { 4 } \right)$ 
C)  $2 \left( 3 x - 4 x ^ { 2 } \right) \left( 9 x ^ { 2 } + 12 x ^ { 3 } + 16 x ^ { 4 } \right)$ 
D)  $2 x ^ { 3 } ( 3 - 4 x ) \left( 9 + 16 x ^ { 2 } \right)$ 
A)  $2 x ^ { 3 } ( 3 - 4 x ) \left( 9 + 12 x + 16 x ^ { 2 } \right)$ 
B)  $2 \left( 3 x + 4 x ^ { 2 } \right) \left( 9 x ^ { 2 } - 12 x ^ { 3 } + 16 x ^ { 4 } \right)$ 
C)  $2 \left( 3 x - 4 x ^ { 2 } \right) \left( 9 x ^ { 2 } + 12 x ^ { 3 } + 16 x ^ { 4 } \right)$ 
D)  $2 x ^ { 3 } ( 3 - 4 x ) \left( 9 + 16 x ^ { 2 } \right)$

Question 10

Factor the trinomial by grouping.
-$4 x ^ { 2 } - 7 x + 4$

Accepted Answer

A)  $( 2 x - 4 ) ( 2 x - 1 )$ 
B)  $( 4 x - 1 ) ( x - 4 )$ 
C)  prime 
D)  $( 4 x - 4 ) ( x - 1 )$ 
A)  $( 2 x - 4 ) ( 2 x - 1 )$ 
B)  $( 4 x - 1 ) ( x - 4 )$ 
C)  prime 
D)  $( 4 x - 4 ) ( x - 1 )$

Question 11

Find the GCF for the list.
-$x ^ { 10 } y ^ { 10 } , x ^ { 9 } y ^ { 9 } , x y ^ { 10 } , x ^ { 5 } y ^ { 6 }$

Accepted Answer

A)  $x ^ { 5 } y ^ { 5 }$ 
B)  $x ^ { 5 } y ^ { 6 }$ 
C)  $x y ^ { 6 }$ 
D)  $x y$ 
A)  $x ^ { 5 } y ^ { 5 }$ 
B)  $x ^ { 5 } y ^ { 6 }$ 
C)  $x y ^ { 6 }$ 
D)  $x y$

Question 12

Solve.
-The equation $D = \frac { 1 } { 2 } \mathrm { n } ( \mathrm { n } - 3 )$ gives the number of diagonals $\mathrm { D }$ for a polygon with $\mathrm { n }$ sides. Find the number of diagonals for a polygon that has 7 sides.

Accepted Answer

A)  4 diagonals 
B)  28 diagonals 
C)  35 diagonals 
D)  14 diagonals 
A)  4 diagonals 
B)  28 diagonals 
C)  35 diagonals 
D)  14 diagonals

Question 13

Factor a negative number or a GCF with a negative coefficient from the polynomial.
-$- 4 x ^ { 4 } + 6 x ^ { 3 } - 2 x ^ { 2 }$

Accepted Answer

A)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } - 3 x - 1 \right)$ 
B)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$ 
C)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } + 3 x + 1 \right)$ 
D)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } + 3 x - 1 \right)$ 
A)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } - 3 x - 1 \right)$ 
B)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$ 
C)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } + 3 x + 1 \right)$ 
D)  $- 2 x ^ { 2 } \left( 2 x ^ { 2 } + 3 x - 1 \right)$

Question 14

Match the equation with its graph.
-$y = ( x - 4 ) ( x + 2 )$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

Write the perimeter of the rectangle as a simplified polynomial. Then factor this polynomial completely.
-

Accepted Answer

A)  $30 x ( x + 4 ) ( x + 2 )$ 
B)  $15 x ( x + 8 ) ( x + 6 )$ 
C)  $15 x ^ { 2 } ( x + 4 ) ( x + 2 )$ 
D)  $30 \left( x ^ { 2 } + 4 \right) ( x + 2 )$ 
A)  $30 x ( x + 4 ) ( x + 2 )$ 
B)  $15 x ( x + 8 ) ( x + 6 )$ 
C)  $15 x ^ { 2 } ( x + 4 ) ( x + 2 )$ 
D)  $30 \left( x ^ { 2 } + 4 \right) ( x + 2 )$

Question 16

Find a positive value of the given variable so that the trinomial is factorable.
-$x ^ { 2 } + b x + 3 ; b = ?$

Accepted Answer

A)  4 
B)  5 
C)  2 
D)  3 
A)  4 
B)  5 
C)  2 
D)  3

Question 17

Factor the four-term polynomial by grouping.
-$6 x ^ { 2 } + 10 x - 9 x - 15$

Accepted Answer

A)  $( 6 x + 3 ) ( x - 5 )$ 
B)  $( 2 x - 3 ) ( 3 x + 5 )$ 
C)  $( 2 x + 3 ) ( 3 x - 5 )$ 
D)  $( 6 x - 3 ) ( x + 5 )$ 
A)  $( 6 x + 3 ) ( x - 5 )$ 
B)  $( 2 x - 3 ) ( 3 x + 5 )$ 
C)  $( 2 x + 3 ) ( 3 x - 5 )$ 
D)  $( 6 x - 3 ) ( x + 5 )$

Question 18

Solve the equation.
-$81 x ^ { 3 } - 16 x = 0$

Accepted Answer

A)  $- \frac { 4 } { 9 }$ 
B)  $\frac { 4 } { 9 }$ 
C)  $\frac { 4 } { 9 } , - \frac { 4 } { 9 }$ 
D)  $\frac { 4 } { 9 } , - \frac { 4 } { 9 } , 0$ 
A)  $- \frac { 4 } { 9 }$ 
B)  $\frac { 4 } { 9 }$ 
C)  $\frac { 4 } { 9 } , - \frac { 4 } { 9 }$ 
D)  $\frac { 4 } { 9 } , - \frac { 4 } { 9 } , 0$

Question 19

Solve.
-A window washer accidentally drops a bucket from the top of a 400-foot building. The height h of the bucket after t seconds is given by h = -16t2 + 400. When will the bucket hit the ground?

Accepted Answer

A)  -5 sec 
B)  80 sec 
C)  5 sec 
D)  25 sec 
A)  -5 sec 
B)  80 sec 
C)  5 sec 
D)  25 sec

Question 20

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$5 a ^ { 2 } + 5 a b - 7 a - 7 b$

Accepted Answer

A)  $( 5 a + 7 ) ( a - b )$ 
B)  $( 5 a - 7 ) ( a - b )$ 
C)  $( 5 a + 7 ) ( a + b )$ 
D)  $( 5 a - 7 ) ( a + b )$ 
A)  $( 5 a + 7 ) ( a - b )$ 
B)  $( 5 a - 7 ) ( a - b )$ 
C)  $( 5 a + 7 ) ( a + b )$ 
D)  $( 5 a - 7 ) ( a + b )$

Factor out the GCF from the polynomial. - $16 m ^ { 9 } + 8 m ^ { 6 } + 10 m ^ { 3 }$

Factor the perfect square trinomial completely. - $49 x ^ { 2 } - 42 x y + 9 y ^ { 2 }$

Solve the equation. - $x ^ { 2 } - 49 = 48 x$

Solve. -Find the length of the shorter leg of a right triangle if the longer leg is 24 meters and the hypotenuse is 6 more than twice the shorter leg.

Factor the four-term polynomial by grouping. - $24 a ^ { 3 } + 30 a ^ { 2 } b - 20 a b ^ { 2 } - 25 b ^ { 3 }$

Factor the binomial completely. - $x ^ { 2 } - \frac { 16 } { 49 }$

Factor the four-term polynomial by grouping. - $x ^ { 3 } + 3 x ^ { 2 } + x + 3$

Factor the binomial completely. - $x ^ { 4 } - 81$

Factor the sum or difference of two cubes. - $54 x ^ { 3 } - 128 x ^ { 6 }$

Factor the trinomial by grouping. - $4 x ^ { 2 } - 7 x + 4$

Find the GCF for the list. - $x ^ { 10 } y ^ { 10 } , x ^ { 9 } y ^ { 9 } , x y ^ { 10 } , x ^ { 5 } y ^ { 6 }$

Solve. -The equation $D = \frac { 1 } { 2 } \mathrm { n } ( \mathrm { n } - 3 )$ gives the number of diagonals $\mathrm { D }$ for a polygon with $\mathrm { n }$ sides. Find the number of diagonals for a polygon that has 7 sides.

Factor a negative number or a GCF with a negative coefficient from the polynomial. - $- 4 x ^ { 4 } + 6 x ^ { 3 } - 2 x ^ { 2 }$

Match the equation with its graph. - $y = ( x - 4 ) ( x + 2 )$

Write the perimeter of the rectangle as a simplified polynomial. Then factor this polynomial completely. -

Find a positive value of the given variable so that the trinomial is factorable. - $x ^ { 2 } + b x + 3 ; b = ?$

Factor the four-term polynomial by grouping. - $6 x ^ { 2 } + 10 x - 9 x - 15$

Solve the equation. - $81 x ^ { 3 } - 16 x = 0$

Solve. -A window washer accidentally drops a bucket from the top of a 400-foot building. The height h of the bucket after t seconds is given by h = -16t2 + 400. When will the bucket hit the ground?

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $5 a ^ { 2 } + 5 a b - 7 a - 7 b$

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Factoring Polynomials

Factor out the GCF from the polynomial. - 16m9+8m6+10m316 m ^ { 9 } + 8 m ^ { 6 } + 10 m ^ { 3 }16m9+8m6+10m3

Factor the perfect square trinomial completely. - 49x2−42xy+9y249 x ^ { 2 } - 42 x y + 9 y ^ { 2 }49x2−42xy+9y2

Solve the equation. - x2−49=48xx ^ { 2 } - 49 = 48 xx2−49=48x