Question 1

Factor.
-$9 x^{4}-18 x^{3}+8 x^{2}$

Accepted Answer

A)  $\left(9 x^{2}+2\right)\left(x^{2}+4\right)$ 
B)  $x^{2}(9 x-1)(x-8)$ 
C)  $x^{2}(3 x-2)(3 x-4)$ 
D)  $x(3 x+2)(3 x+4)$ 
A)  $\left(9 x^{2}+2\right)\left(x^{2}+4\right)$ 
B)  $x^{2}(9 x-1)(x-8)$ 
C)  $x^{2}(3 x-2)(3 x-4)$ 
D)  $x(3 x+2)(3 x+4)$

Question 2

Factor using the ac-method.
-$10 y^{4}-19 y^{2}-15$

Accepted Answer

A)  $\left(2 y^{2}-5\right)\left(5 y^{2}+3\right)$ 
B)  $\left(10 y^{2}-5\right)\left(y^{2}+3\right)$ 
C)  $\left(2 y^{2}+1\right)\left(5 y^{2}-15\right)$ 
D)  $(5 y-3)(2 y+5)$ 
A)  $\left(2 y^{2}-5\right)\left(5 y^{2}+3\right)$ 
B)  $\left(10 y^{2}-5\right)\left(y^{2}+3\right)$ 
C)  $\left(2 y^{2}+1\right)\left(5 y^{2}-15\right)$ 
D)  $(5 y-3)(2 y+5)$

Question 3

Factor.
-$6 x^{2}-26 x-20$

Accepted Answer

A)  $2(3 x+2)(x-5)$ 
B)  $2(3 x-2)(x+5)$ 
C)  $(3 x+2)(2 x-10)$ 
D)  $(6 x+4)(x-5)$ 
A)  $2(3 x+2)(x-5)$ 
B)  $2(3 x-2)(x+5)$ 
C)  $(3 x+2)(2 x-10)$ 
D)  $(6 x+4)(x-5)$

Question 4

Factor.
-$x^{2}-0.9 x+0.2$

Accepted Answer

A)  $(x-0.4)(x+0.5)$ 
B)  $(x-0.4)(x-0.5)$ 
C)  $(x+0.4)(x-0.5)$ 
D)  $(x-0.45)^{2}$ 
A)  $(x-0.4)(x+0.5)$ 
B)  $(x-0.4)(x-0.5)$ 
C)  $(x+0.4)(x-0.5)$ 
D)  $(x-0.45)^{2}$

Question 5

Solve the problem.
-The length of a rectangular frame is $3 \mathrm{~cm}$ more than the width. The area inside the frame is 40 square $\mathrm{cm}$. Find the width of the frame.

Accepted Answer

A)  $6 \mathrm{~cm}$ 
B)  $8 \mathrm{~cm}$ 
C)  $11 \mathrm{~cm}$ 
D)  $5 \mathrm{~cm}$ 
A)  $6 \mathrm{~cm}$ 
B)  $8 \mathrm{~cm}$ 
C)  $11 \mathrm{~cm}$ 
D)  $5 \mathrm{~cm}$

Question 6

Factor using the ac-method.
-$96 x^{2}+56 x y+8 y^{2}$

Accepted Answer

A)  $8(3 x-y)(4 x-y)$ 
B)  prime 
C)  $8(3 x+y)(4 x+y)$ 
D)  $(24 x+8 y)(4 x+y)$ 
A)  $8(3 x-y)(4 x-y)$ 
B)  prime 
C)  $8(3 x+y)(4 x+y)$ 
D)  $(24 x+8 y)(4 x+y)$

Question 7

Solve by factoring and using the principle of zero products.
-$2 k^{2}-13 k-7=0$

Accepted Answer

A)  $\frac{1}{13},-\frac{1}{2}$ 
B)  $-2,7$ 
C)  $-\frac{1}{2}, 2$ 
D)  $-\frac{1}{2}, 7$ 
A)  $\frac{1}{13},-\frac{1}{2}$ 
B)  $-2,7$ 
C)  $-\frac{1}{2}, 2$ 
D)  $-\frac{1}{2}, 7$

Question 8

Factor.
-$y^{2}+1.4 y+0.49$

Accepted Answer

A)  $(y+1.4)^{2}$ 
B)  $y(y+1.4)$ 
C)  $(y+0.7)^{2}$ 
D)  $\left(y^{2}+0.7\right)^{2}$ 
A)  $(y+1.4)^{2}$ 
B)  $y(y+1.4)$ 
C)  $(y+0.7)^{2}$ 
D)  $\left(y^{2}+0.7\right)^{2}$

Question 9

Factor.
-$x^{2}+8 x-48$

Accepted Answer

A)  $(x+12)(x-4)$ 
B)  $(x-12)(x+1)$ 
C)  Prime 
D)  $(x-12)(x+4)$ 
A)  $(x+12)(x-4)$ 
B)  $(x-12)(x+1)$ 
C)  Prime 
D)  $(x-12)(x+4)$

Question 10

Factor.
-$3 x(6 x+5)-2(6 x+5)$

Accepted Answer

A)  $(3 x+2)(6 x-5)$ 
B)  $(18 x+2)(x-5)$ 
C)  $(18 x-2)(x+5)$ 
D)  $(3 x-2)(6 x+5)$ 
A)  $(3 x+2)(6 x-5)$ 
B)  $(18 x+2)(x-5)$ 
C)  $(18 x-2)(x+5)$ 
D)  $(3 x-2)(6 x+5)$

Question 11

Solve by factoring and using the principle of zero products.
-$\mathrm{x}(\mathrm{x}-6)=16$

Accepted Answer

A)  2,8 
B)  $-2,-8$ 
C)  $2,-8$ 
D)  $-2,8$ 
A)  2,8 
B)  $-2,-8$ 
C)  $2,-8$ 
D)  $-2,8$

Question 12

Determine whether the following is a difference of squares.
-$x^{2}-4 y^{2}$

Accepted Answer

A) True 
 B)False

Question 13

Factor.
-$x^{2}-x-54$

Accepted Answer

A)  $(x-6)(x+9)$ 
B)  Prime 
C)  $(x-54)(x+1)$ 
D)  $(x+6)(x-9)$ 
A)  $(x-6)(x+9)$ 
B)  Prime 
C)  $(x-54)(x+1)$ 
D)  $(x+6)(x-9)$

Question 14

Factor.
-$20 x^{2}-23 x y+6 y^{2}$

Accepted Answer

A)  $(4 x+3 y)(5 x-2 y)$ 
B)  $(4 x-3 y)(5 x-2 y)$ 
C)  $(20 x+3 y)(x+2 y)$ 
D)  $(4 x+3 y)(5 x+2 y)$ 
A)  $(4 x+3 y)(5 x-2 y)$ 
B)  $(4 x-3 y)(5 x-2 y)$ 
C)  $(20 x+3 y)(x+2 y)$ 
D)  $(4 x+3 y)(5 x+2 y)$

Question 15

Solve the problem.
-Within a group of $n$ people, the number of possible handshakes, $N$, is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$. At a party, everybody shakes hands with every other person. If the total number of handshakes is 28 , how many people are at the party?

Accepted Answer

A)  8 
B)  10 
C)  7 
D)  9 
A)  8 
B)  10 
C)  7 
D)  9

Factor. - $9 x^{4}-18 x^{3}+8 x^{2}$

Factor using the ac-method. - $10 y^{4}-19 y^{2}-15$

Factor. - $6 x^{2}-26 x-20$

Factor. - $x^{2}-0.9 x+0.2$

Solve the problem. -The length of a rectangular frame is $3 \mathrm{~cm}$ more than the width. The area inside the frame is 40 square $\mathrm{cm}$ . Find the width of the frame.

Factor using the ac-method. - $96 x^{2}+56 x y+8 y^{2}$

Solve by factoring and using the principle of zero products. - $2 k^{2}-13 k-7=0$

Factor. - $y^{2}+1.4 y+0.49$

Factor. - $x^{2}+8 x-48$

Factor. - $3 x(6 x+5)-2(6 x+5)$

Solve by factoring and using the principle of zero products. - $\mathrm{x}(\mathrm{x}-6)=16$

Determine whether the following is a difference of squares. - $x^{2}-4 y^{2}$

Factor. - $x^{2}-x-54$

Factor. - $20 x^{2}-23 x y+6 y^{2}$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Systems of Equations

Radical Expressions and Equations

Quadratic Equations

Equations of Lines and Simplifying Radical Expressions

Filters

Exam 5: Polynomials: Factoring

Factor. - 9x4−18x3+8x29 x^{4}-18 x^{3}+8 x^{2}9x4−18x3+8x2

Factor using the ac-method. - 10y4−19y2−1510 y^{4}-19 y^{2}-1510y4−19y2−15

Factor. - 6x2−26x−206 x^{2}-26 x-206x2−26x−20

Factor. - x2−0.9x+0.2x^{2}-0.9 x+0.2x2−0.9x+0.2

Solve the problem. -The length of a rectangular frame is 3 cm3 \mathrm{~cm}3 cm more than the width. The area inside the frame is 40 square cm\mathrm{cm}cm . Find the width of the frame.

Factor using the ac-method. - 96x2+56xy+8y296 x^{2}+56 x y+8 y^{2}96x2+56xy+8y2

Solve by factoring and using the principle of zero products. - 2k2−13k−7=02 k^{2}-13 k-7=02k2−13k−7=0

Factor. - y2+1.4y+0.49y^{2}+1.4 y+0.49y2+1.4y+0.49

Factor. - x2+8x−48x^{2}+8 x-48x2+8x−48

Factor. - 3x(6x+5)−2(6x+5)3 x(6 x+5)-2(6 x+5)3x(6x+5)−2(6x+5)

Solve by factoring and using the principle of zero products. - x(x−6)=16\mathrm{x}(\mathrm{x}-6)=16x(x−6)=16

Determine whether the following is a difference of squares. - x2−4y2x^{2}-4 y^{2}x2−4y2

Factor. - x2−x−54x^{2}-x-54x2−x−54

Factor. - 20x2−23xy+6y220 x^{2}-23 x y+6 y^{2}20x2−23xy+6y2