Question 1

Solve the equation.
-$\left( x + \frac { 1 } { 7 } \right) \left( x - \frac { 4 } { 5 } \right) = 0$

Accepted Answer

A)  $7 , \frac { 5 } { 4 }$ 
B)  6,1 
C)  $- \frac { 1 } { 7 } , \frac { 4 } { 5 }$ 
D)  $\frac { 1 } { 7 } , - \frac { 4 } { 5 }$ 
A)  $7 , \frac { 5 } { 4 }$ 
B)  6,1 
C)  $- \frac { 1 } { 7 } , \frac { 4 } { 5 }$ 
D)  $\frac { 1 } { 7 } , - \frac { 4 } { 5 }$

Question 2

Factor the polynomial by grouping.
-$3 x ^ { 2 } + 2 x + 6 x + 4$

Accepted Answer

A)  $( 3 x + 2 ) ( 3 x + 2 )$ 
B)  $( x + 2 ) ( 3 x + 2 )$ 
C)  $( 3 x + 2 ) ( 2 x + 3 )$ 
D)  prime 
A)  $( 3 x + 2 ) ( 3 x + 2 )$ 
B)  $( x + 2 ) ( 3 x + 2 )$ 
C)  $( 3 x + 2 ) ( 2 x + 3 )$ 
D)  prime

Question 3

Solve the equation.
-$x ( x - 6 ) = 40$

Accepted Answer

A)  0,6 
B)  $4 , - 10$ 
C)  $- 4,10$ 
D)  4,10 
A)  0,6 
B)  $4 , - 10$ 
C)  $- 4,10$ 
D)  4,10

Question 4

Factor the perfect square trinomial completely.
-$25 x ^ { 2 } - 70 x + 49$

Accepted Answer

A)  $( 25 x + 1 ) ( x + 49 )$ 
B)  $( 5 x - 7 ) ^ { 2 }$ 
C)  $( 5 x - 7 ) ( 5 x + 7 )$ 
D)  $( 5 x + 7 ) ^ { 2 }$ 
A)  $( 25 x + 1 ) ( x + 49 )$ 
B)  $( 5 x - 7 ) ^ { 2 }$ 
C)  $( 5 x - 7 ) ( 5 x + 7 )$ 
D)  $( 5 x + 7 ) ^ { 2 }$

Question 5

Factor the polynomial completely. If the polynomial cannot be factored, write "prime."
-$y ^ { 2 } - 6 y - 55$

Accepted Answer

A)  $( y - 11 ) ( y + 5 )$ 
B)  $( y + 11 ) ( y - 5 )$ 
C)  prime 
D)  $( \mathrm { y } - 55 ) ( \mathrm { y } + 1 )$ 
A)  $( y - 11 ) ( y + 5 )$ 
B)  $( y + 11 ) ( y - 5 )$ 
C)  prime 
D)  $( \mathrm { y } - 55 ) ( \mathrm { y } + 1 )$

Question 6

Find the GCF for the list.
-$x ^ { 2 } , x ^ { 5 } , x ^ { 5 }$

Accepted Answer

A)  $x$ 
B)  $x ^ { 5 }$ 
C)  $x ^ { 12 }$ 
D)  $x ^ { 2 }$ 
A)  $x$ 
B)  $x ^ { 5 }$ 
C)  $x ^ { 12 }$ 
D)  $x ^ { 2 }$

Question 7

Factor completely.
-$- 3 x ^ { 2 } - 13 x + 10$

Accepted Answer

A)  $- 1 ( 3 x + 2 ) ( x - 5 )$ 
B)  $- 1 ( 3 x + 5 ) ( x - 2 )$ 
C)  prime 
D)  $- 1 ( 3 x - 2 ) ( x + 5 )$ 
A)  $- 1 ( 3 x + 2 ) ( x - 5 )$ 
B)  $- 1 ( 3 x + 5 ) ( x - 2 )$ 
C)  prime 
D)  $- 1 ( 3 x - 2 ) ( x + 5 )$

Question 8

Factor the binomial completely.
-$9 x ^ { 2 } - 4$

Accepted Answer

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

Question 9

Solve.
-If the cost, $C ( x )$, for manufacturing $x$ units of a certain product is given by $C ( x ) = x ^ { 2 } - 50 x + 5000$, find the number of units manufactured at a cost of $\$ 7400$.

Accepted Answer

A)  80 units 
B)  30 units 
C)  50 units 
D)  100 units 
A)  80 units 
B)  30 units 
C)  50 units 
D)  100 units

Question 10

Factor out the GCF from the polynomial.
-$28 x ^ { 8 } y ^ { 8 } + 32 x ^ { 5 } y ^ { 6 } - 32 x ^ { 3 } y ^ { 3 }$

Accepted Answer

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

Question 11

Solve the equation.
-$12 x ^ { 2 } + 31 x + 13 = - 7$

Accepted Answer

A)  $\frac { 4 } { 5 } , \frac { 3 } { 4 }$ 
B)  $- \frac { 5 } { 4 } , - \frac { 4 } { 3 }$ 
C)  $\frac { 5 } { 4 } , \frac { 4 } { 3 }$ 
D)  $- \frac { 4 } { 5 } , - \frac { 4 } { 3 }$ 
A)  $\frac { 4 } { 5 } , \frac { 3 } { 4 }$ 
B)  $- \frac { 5 } { 4 } , - \frac { 4 } { 3 }$ 
C)  $\frac { 5 } { 4 } , \frac { 4 } { 3 }$ 
D)  $- \frac { 4 } { 5 } , - \frac { 4 } { 3 }$

Question 12

Find the GCF for the list.
-$21 \mathrm {~m} ^ { 4 } , 189 \mathrm {~m} ^ { 7 } , 441 \mathrm {~m} ^ { 5 }$

Accepted Answer

A)  $21 \mathrm {~m} ^ { 3 }$ 
B)  $21 \mathrm {~m} ^ { 4 }$ 
C)  $3969 \mathrm {~m} ^ { 3 }$ 
D)  $189 \mathrm {~m} ^ { 4 }$ 
A)  $21 \mathrm {~m} ^ { 3 }$ 
B)  $21 \mathrm {~m} ^ { 4 }$ 
C)  $3969 \mathrm {~m} ^ { 3 }$ 
D)  $189 \mathrm {~m} ^ { 4 }$

Question 13

Factor completely.
-$4 y ^ { 2 } + 18 y - 10$

Accepted Answer

A)  prime 
B)  $2 ( 2 y - 1 ) ( y + 5 )$ 
C)  $2 ( 2 y + 1 ) ( y - 5 )$ 
D)  $( 4 y - 2 ) ( y + 5 )$ 
A)  prime 
B)  $2 ( 2 y - 1 ) ( y + 5 )$ 
C)  $2 ( 2 y + 1 ) ( y - 5 )$ 
D)  $( 4 y - 2 ) ( y + 5 )$

Question 14

Factor the four-term polynomial by grouping.
-$x y + 9 x - 5 y - 45$

Accepted Answer

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

Question 15

Represent each given condition using a single variable, x.
-Three consecutive odd integers

Accepted Answer

A)  x and x + 2, if x is an odd integer 
B)  x, x + 2, and x + 4, if x is an odd integer 
C)  x, x + 1, and x + 2, if x is an odd integer 
D)  x + 2, x + 4, and x + 6, if x is an odd integer 
A)  x and x + 2, if x is an odd integer 
B)  x, x + 2, and x + 4, if x is an odd integer 
C)  x, x + 1, and x + 2, if x is an odd integer 
D)  x + 2, x + 4, and x + 6, if x is an odd integer

Question 16

Factor completely.
-$7 a ^ { 5 } + 50 a ^ { 3 } b ^ { 2 } + 7 a b ^ { 4 }$

Accepted Answer

A)  $a \left( 7 a ^ { 2 } + 7 b ^ { 2 } \right) ^ { 2 }$ 
B)  prime 
C)  $a \left( 7 a ^ { 2 } + b ^ { 2 } \right) ^ { 2 }$ 
D)  $a \left( 7 a ^ { 2 } + b ^ { 2 } \right) \left( a ^ { 2 } + 7 b ^ { 2 } \right)$ 
A)  $a \left( 7 a ^ { 2 } + 7 b ^ { 2 } \right) ^ { 2 }$ 
B)  prime 
C)  $a \left( 7 a ^ { 2 } + b ^ { 2 } \right) ^ { 2 }$ 
D)  $a \left( 7 a ^ { 2 } + b ^ { 2 } \right) \left( a ^ { 2 } + 7 b ^ { 2 } \right)$

Question 17

Factor the binomial completely.
-$s ^ { 2 } b ^ { 2 } - 1$

Accepted Answer

A)  $( s b + 1 ) ( s b - 1 )$ 
B)  $( s b - 1 ) ^ { 2 }$ 
C)  $( s b + 1 ) ^ { 2 }$ 
D)  prime 
A)  $( s b + 1 ) ( s b - 1 )$ 
B)  $( s b - 1 ) ^ { 2 }$ 
C)  $( s b + 1 ) ^ { 2 }$ 
D)  prime

Question 18

Factor the sum or difference of two cubes.
-$64 p ^ { 3 } - 1$

Accepted Answer

A)  $( 4 p - 1 ) \left( 16 p ^ { 2 } + 1 \right)$ 
B)  $( 64 p - 1 ) \left( p ^ { 2 } + 4 p + 1 \right)$ 
C)  $( 4 p - 1 ) \left( 16 p ^ { 2 } + 4 p + 1 \right)$ 
D)  $( 4 p + 1 ) \left( 16 p ^ { 2 } - 4 p + 1 \right)$ 
A)  $( 4 p - 1 ) \left( 16 p ^ { 2 } + 1 \right)$ 
B)  $( 64 p - 1 ) \left( p ^ { 2 } + 4 p + 1 \right)$ 
C)  $( 4 p - 1 ) \left( 16 p ^ { 2 } + 4 p + 1 \right)$ 
D)  $( 4 p + 1 ) \left( 16 p ^ { 2 } - 4 p + 1 \right)$

Question 19

Solve the equation.
-$x ( 9 x + 3 ) = 0$

Accepted Answer

A)  0,3 
B)  $0 , - \frac { 1 } { 3 }$ 
C)  $0 , \frac { 1 } { 3 }$ 
D)  $0 , - 3$ 
A)  0,3 
B)  $0 , - \frac { 1 } { 3 }$ 
C)  $0 , \frac { 1 } { 3 }$ 
D)  $0 , - 3$

Question 20

Factor the binomial completely.
-$144 - x ^ { 2 } y ^ { 2 }$

Accepted Answer

A)  $( 12 - x y ) ^ { 2 }$ 
B)  $( 12 + x y ) ^ { 2 }$ 
C)  prime 
D)  $( 12 - x y ) ( 12 + x y )$ 
A)  $( 12 - x y ) ^ { 2 }$ 
B)  $( 12 + x y ) ^ { 2 }$ 
C)  prime 
D)  $( 12 - x y ) ( 12 + x y )$

Solve the equation. - $\left( x + \frac { 1 } { 7 } \right) \left( x - \frac { 4 } { 5 } \right) = 0$

Factor the polynomial by grouping. - $3 x ^ { 2 } + 2 x + 6 x + 4$

Solve the equation. - $x ( x - 6 ) = 40$

Factor the perfect square trinomial completely. - $25 x ^ { 2 } - 70 x + 49$

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - $y ^ { 2 } - 6 y - 55$

Find the GCF for the list. - $x ^ { 2 } , x ^ { 5 } , x ^ { 5 }$

Factor completely. - $- 3 x ^ { 2 } - 13 x + 10$

Factor the binomial completely. - $9 x ^ { 2 } - 4$

Solve. -If the cost, $C ( x )$ , for manufacturing $x$ units of a certain product is given by $C ( x ) = x ^ { 2 } - 50 x + 5000$ , find the number of units manufactured at a cost of $\$ 7400$ .

Factor out the GCF from the polynomial. - $28 x ^ { 8 } y ^ { 8 } + 32 x ^ { 5 } y ^ { 6 } - 32 x ^ { 3 } y ^ { 3 }$

Solve the equation. - $12 x ^ { 2 } + 31 x + 13 = - 7$

Find the GCF for the list. - $21 \mathrm {~m} ^ { 4 } , 189 \mathrm {~m} ^ { 7 } , 441 \mathrm {~m} ^ { 5 }$

Factor completely. - $4 y ^ { 2 } + 18 y - 10$

Factor the four-term polynomial by grouping. - $x y + 9 x - 5 y - 45$

Represent each given condition using a single variable, x. -Three consecutive odd integers

Factor completely. - $7 a ^ { 5 } + 50 a ^ { 3 } b ^ { 2 } + 7 a b ^ { 4 }$

Factor the binomial completely. - $s ^ { 2 } b ^ { 2 } - 1$

Factor the sum or difference of two cubes. - $64 p ^ { 3 } - 1$

Solve the equation. - $x ( 9 x + 3 ) = 0$

Factor the binomial completely. - $144 - x ^ { 2 } y ^ { 2 }$

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

Solve the equation. - (x+17)(x−45)=0\left( x + \frac { 1 } { 7 } \right) \left( x - \frac { 4 } { 5 } \right) = 0(x+71​)(x−54​)=0

Factor the polynomial by grouping. - 3x2+2x+6x+43 x ^ { 2 } + 2 x + 6 x + 43x2+2x+6x+4

Solve the equation. - x(x−6)=40x ( x - 6 ) = 40x(x−6)=40

Factor the perfect square trinomial completely. - 25x2−70x+4925 x ^ { 2 } - 70 x + 4925x2−70x+49

Factor the polynomial completely. If the polynomial cannot be factored, write "prime." - y2−6y−55y ^ { 2 } - 6 y - 55y2−6y−55

Find the GCF for the list. - x2,x5,x5x ^ { 2 } , x ^ { 5 } , x ^ { 5 }x2,x5,x5

Factor completely. - −3x2−13x+10- 3 x ^ { 2 } - 13 x + 10−3x2−13x+10

Factor the binomial completely. - 9x2−49 x ^ { 2 } - 49x2−4

Solve. -If the cost, C(x)C ( x )C(x) , for manufacturing xxx units of a certain product is given by C(x)=x2−50x+5000C ( x ) = x ^ { 2 } - 50 x + 5000C(x)=x2−50x+5000 , find the number of units manufactured at a cost of $7400\$ 7400$7400 .

Factor out the GCF from the polynomial. - 28x8y8+32x5y6−32x3y328 x ^ { 8 } y ^ { 8 } + 32 x ^ { 5 } y ^ { 6 } - 32 x ^ { 3 } y ^ { 3 }28x8y8+32x5y6−32x3y3

Solve the equation. - 12x2+31x+13=−712 x ^ { 2 } + 31 x + 13 = - 712x2+31x+13=−7

Find the GCF for the list. - 21 m4,189 m7,441 m521 \mathrm {~m} ^ { 4 } , 189 \mathrm {~m} ^ { 7 } , 441 \mathrm {~m} ^ { 5 }21 m4,189 m7,441 m5

Factor completely. - 4y2+18y−104 y ^ { 2 } + 18 y - 104y2+18y−10

Factor the four-term polynomial by grouping. - xy+9x−5y−45x y + 9 x - 5 y - 45xy+9x−5y−45