Question 1

Factor.
-$3 x^{6}-33 x^{5}+90 x^{4}$

Accepted Answer

A)  $3 x^{4}(x+6)(x-5)$ 
B)  $3 x^{4}(x+6)(x+5)$ 
C)  $3 x^{4}(x-6)(x+5)$ 
D)  $3 x^{4}(x-6)(x-5)$ 
A)  $3 x^{4}(x+6)(x-5)$ 
B)  $3 x^{4}(x+6)(x+5)$ 
C)  $3 x^{4}(x-6)(x+5)$ 
D)  $3 x^{4}(x-6)(x-5)$

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-How could you solve the equation ((7 x+5)(2 x-9)(8 x-6)=0\) ? How many equations do you need to solve? What are their solutions?

Accepted Answer

Set each factor equa

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain the error in the following:
$x^{2}+2 x-15=(x-5)(x+3)$

Accepted Answer

The factorization yi

Question 4

Factor using the ac-method.
-$6 x^{2}+17 x+12$

Accepted Answer

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

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-A student is trying to solve the equation $(x+5)(x-9)=4$. The student has set $x+5=4$ and $x-9=4$ and found that two solutions $x=-1, x=13$. The student checks his or her results by plugging in his or her solutions into the original equation and finds that they do not work. How would you advise him or her?

Accepted Answer

The equation needs t

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Explain the error in the following:
$x^{2}-y^{2}=(x-y)^{2}$

Accepted Answer

x² - y² is a differenc

Question 7

Solve the problem.
-A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A)  150 meters 
B)  90 meters 
C)  120 meters 
D)  180 meters 
A)  150 meters 
B)  90 meters 
C)  120 meters 
D)  180 meters

Question 8

Determine whether the following is a difference of squares.
-$t^{3}-9$

Accepted Answer

A) True 
 B)False

Question 9

Solve by factoring and using the principle of zero products.
-$x^{2}-x=56$

Accepted Answer

A)  $-7,-8$ 
B)  7,8 
C)  $-7,8$ 
D)  1,56 
A)  $-7,-8$ 
B)  7,8 
C)  $-7,8$ 
D)  1,56

Question 10

Determine whether the following is a trinomial square.
-$x^{2}-8 x-16$

Accepted Answer

A) True 
 B)False

Question 11

Solve using the principle of zero products.
-$\frac{3}{8} z\left(z-\frac{1}{6}\right)=0$

Accepted Answer

A)  $-\frac{3}{8}, \frac{1}{6}$ 
B)  $\frac{1}{6}, 0$ 
C)  $\frac{3}{8}, \frac{1}{6}$ 
D)  $-\frac{1}{6}, 0$ 
A)  $-\frac{3}{8}, \frac{1}{6}$ 
B)  $\frac{1}{6}, 0$ 
C)  $\frac{3}{8}, \frac{1}{6}$ 
D)  $-\frac{1}{6}, 0$

Question 12

Factor.
-$t^{2}+0.2 t-0.15$

Accepted Answer

A)  $(t+0.15)(t-1)$ 
B)  $(t+0.1)^{2}$ 
C)  $(t-0.5)(t+0.3)$ 
D)  $(t+0.5)(t-0.3)$ 
A)  $(t+0.15)(t-1)$ 
B)  $(t+0.1)^{2}$ 
C)  $(t-0.5)(t+0.3)$ 
D)  $(t+0.5)(t-0.3)$

Question 13

Solve using the principle of zero products.
-$\left(5 x-\frac{1}{4}\right)\left(x+\frac{1}{5}\right)=0$

Accepted Answer

A)  $-\frac{1}{20},-\frac{1}{5}$ 
B)  $-\frac{1}{20}, \frac{1}{5}$ 
C)  $\frac{1}{20},-\frac{1}{5}$ 
D)  $\frac{1}{20}, \frac{1}{5}$ 
A)  $-\frac{1}{20},-\frac{1}{5}$ 
B)  $-\frac{1}{20}, \frac{1}{5}$ 
C)  $\frac{1}{20},-\frac{1}{5}$ 
D)  $\frac{1}{20}, \frac{1}{5}$

Question 14

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

Accepted Answer

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

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Use the FOIL method to show that $(7 x+14)(x-4)$ is $7 x^{2}-14 x-56$. If you were asked to completely factor $7 x^{2}-14 x-56$, why would it be incorrect to give $(7 x+14)(x-4)$ as your answer?

Accepted Answer

The factor

Question 16

Determine whether the following is a difference of squares.
-$42 x^{2}-y^{2}$

Accepted Answer

A) True 
 B)False

Question 17

Factor.
-$12 z^{3}+7 z^{2}-12 z$

Accepted Answer

A)  $\left(z^{2}-3\right)(12 z+4)$ 
B)  $(3 z-4)(4 z+3)$ 
C)  $z(3 z+4)(4 z-3)$ 
D)  $z(12 z+1)(z-12)$ 
A)  $\left(z^{2}-3\right)(12 z+4)$ 
B)  $(3 z-4)(4 z+3)$ 
C)  $z(3 z+4)(4 z-3)$ 
D)  $z(12 z+1)(z-12)$

Question 18

Factor using the ac-method.
-$-48 x^{2}-40 x+48$

Accepted Answer

A)  $-8(3 x+2)(2 x-3)$ 
B)  $-8(3 x-2)(2 x+3)$ 
C)  $(-24 x+16)(2 x+3)$ 
D)  prime 
A)  $-8(3 x+2)(2 x-3)$ 
B)  $-8(3 x-2)(2 x+3)$ 
C)  $(-24 x+16)(2 x+3)$ 
D)  prime

Question 19

Determine whether the following is a trinomial square.
-$27 x^{2}-117 x-90$

Accepted Answer

A) True 
 B)False

Question 20

Determine whether the following is a difference of squares.
-$144 x^{2}-49 y^{2}$

Accepted Answer

A) True 
 B)False

Factor. - $3 x^{6}-33 x^{5}+90 x^{4}$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -How could you solve the equation ((7 x+5)(2 x-9)(8 x-6)=0\) ? How many equations do you need to solve? What are their solutions?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: $x^{2}+2 x-15=(x-5)(x+3)$

Factor using the ac-method. - $6 x^{2}+17 x+12$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: $x^{2}-y^{2}=(x-y)^{2}$

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?

Determine whether the following is a difference of squares. - $t^{3}-9$

Solve by factoring and using the principle of zero products. - $x^{2}-x=56$

Determine whether the following is a trinomial square. - $x^{2}-8 x-16$

Solve using the principle of zero products. - $\frac{3}{8} z\left(z-\frac{1}{6}\right)=0$

Factor. - $t^{2}+0.2 t-0.15$

Solve using the principle of zero products. - $\left(5 x-\frac{1}{4}\right)\left(x+\frac{1}{5}\right)=0$

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

Determine whether the following is a difference of squares. - $42 x^{2}-y^{2}$

Factor. - $12 z^{3}+7 z^{2}-12 z$

Factor using the ac-method. - $-48 x^{2}-40 x+48$

Determine whether the following is a trinomial square. - $27 x^{2}-117 x-90$

Determine whether the following is a difference of squares. - $144 x^{2}-49 y^{2}$

Whole Numbers

Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

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

Converting Units of Measurement

Filters

Exam 11: Polynomials: Factoring

Factor. - 3x6−33x5+90x43 x^{6}-33 x^{5}+90 x^{4}3x6−33x5+90x4

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -How could you solve the equation ((7 x+5)(2 x-9)(8 x-6)=0\) ? How many equations do you need to solve? What are their solutions?

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: x2+2x−15=(x−5)(x+3)x^{2}+2 x-15=(x-5)(x+3)x2+2x−15=(x−5)(x+3)

Factor using the ac-method. - 6x2+17x+126 x^{2}+17 x+126x2+17x+12

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: x2−y2=(x−y)2x^{2}-y^{2}=(x-y)^{2}x2−y2=(x−y)2

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 90 meters. The hypotenuse is 30 meters longer than the length of the longer leg. How long is the longer leg?

Determine whether the following is a difference of squares. - t3−9t^{3}-9t3−9

Solve by factoring and using the principle of zero products. - x2−x=56x^{2}-x=56x2−x=56

Determine whether the following is a trinomial square. - x2−8x−16x^{2}-8 x-16x2−8x−16

Solve using the principle of zero products. - 38z(z−16)=0\frac{3}{8} z\left(z-\frac{1}{6}\right)=083​z(z−61​)=0

Factor. - t2+0.2t−0.15t^{2}+0.2 t-0.15t2+0.2t−0.15

Solve using the principle of zero products. - (5x−14)(x+15)=0\left(5 x-\frac{1}{4}\right)\left(x+\frac{1}{5}\right)=0(5x−41​)(x+51​)=0

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

Determine whether the following is a difference of squares. - 42x2−y242 x^{2}-y^{2}42x2−y2

Factor. - 12z3+7z2−12z12 z^{3}+7 z^{2}-12 z12z3+7z2−12z

Factor using the ac-method. - −48x2−40x+48-48 x^{2}-40 x+48−48x2−40x+48

Determine whether the following is a trinomial square. - 27x2−117x−9027 x^{2}-117 x-9027x2−117x−90

Determine whether the following is a difference of squares. - 144x2−49y2144 x^{2}-49 y^{2}144x2−49y2

Whole Numbers

Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

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

Converting Units of Measurement

Filters

Factor. - $3 x^{6}-33 x^{5}+90 x^{4}$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: $x^{2}+2 x-15=(x-5)(x+3)$

Factor using the ac-method. - $6 x^{2}+17 x+12$

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: $x^{2}-y^{2}=(x-y)^{2}$

Determine whether the following is a difference of squares. - $t^{3}-9$

Solve by factoring and using the principle of zero products. - $x^{2}-x=56$

Determine whether the following is a trinomial square. - $x^{2}-8 x-16$

Solve using the principle of zero products. - $\frac{3}{8} z\left(z-\frac{1}{6}\right)=0$

Factor. - $t^{2}+0.2 t-0.15$

Solve using the principle of zero products. - $\left(5 x-\frac{1}{4}\right)\left(x+\frac{1}{5}\right)=0$

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

Determine whether the following is a difference of squares. - $42 x^{2}-y^{2}$

Factor. - $12 z^{3}+7 z^{2}-12 z$

Factor using the ac-method. - $-48 x^{2}-40 x+48$

Determine whether the following is a trinomial square. - $27 x^{2}-117 x-90$

Determine whether the following is a difference of squares. - $144 x^{2}-49 y^{2}$