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01/14 1. Algebraic Foundations and Factoring Online Quiz Questions

Use this free practice quiz with 20 questions to review 01/14 1. Algebraic Foundations and Factoring, test your knowledge, and prepare for your next test or exam.

20 questions
01
Choose one
1 point

Evaluate 18−2[32−(4+1)]18-2[3^2-(4+1)].

  1. A

    8

  2. B

    10

  3. C

    14

  4. D

    26

02
True or false
1 point

True or false: 3x+63x+6 is an equation because it contains a variable.

  1. A

    True

  2. B

    False

03
Written response
1 point

Evaluate 3x2−4x+13x^2-4x+1 when x=−2x=-2. Enter the numerical value as an integer.

04
Fill in the blank
1 point

Identify the three terms in 4x2−3x+94x^2-3x+9: , , and .

05
Choose one
1 point

Which property of equality justifies changing a=ba=b into b=ab=a?

  1. A

    Reflexive Property

  2. B

    Transitive Property

  3. C

    Symmetric Property

  4. D

    Distributive Property

06
Choose all
1 point

Select all the rational numbers.

  1. A

    −6-6

  2. B

    2\sqrt{2}

  3. C

    0.1250.125

  4. D

    π\pi

07
True or false
1 point

True or false: x2+9x^2+9 cannot be factored over the real numbers.

  1. A

    True

  2. B

    False

08
Written response
1 point

Factor 12x3+18x212x^3+18x^2 completely. Enter the factored expression.

09
Choose one
1 point

Factor 6x2+11x+36x^2+11x+3 completely.

  1. A

    (6x+1)(x+3)(6x+1)(x+3)

  2. B

    (3x+1)(2x+3)(3x+1)(2x+3)

  3. C

    (3x+3)(2x+1)(3x+3)(2x+1)

  4. D

    (6x+3)(x+1)(6x+3)(x+1)

10
Choose all
1 point

Select all expressions that can be factored directly using the difference-of-squares identity.

  1. A

    25x2−4925x^2-49

  2. B

    x2−16x^2-16

  3. C

    x2+9x^2+9

  4. D

    8x3−18x^3-1

11
Choose one
1 point

Solve 3x3−12x=03x^3-12x=0.

  1. A

    x=0,2x=0,2

  2. B

    x=−2,0,2x=-2,0,2

  3. C

    x=−4,0,4x=-4,0,4

  4. D

    x=−2,2x=-2,2

12
Open ended
1 point

Solve x2−5x+6=0x^2-5x+6=0 by factoring. Show the factorization and explain how it leads to all solutions.

13
Choose one
1 point

Evaluate 18−2[32−(4+1)]18-2[3^2-(4+1)].

  1. A

    8

  2. B

    10

  3. C

    14

  4. D

    22

14
Choose one
1 point

Which number is irrational?

  1. A

    34\frac{3}{4}

  2. B

    −6-6

  3. C

    5\sqrt{5}

  4. D

    0.1250.125

15
True or false
1 point

True or false: 3x+63x+6 is an equation because it contains a variable.

  1. A

    True

  2. B

    False

16
Choose one
1 point

Which property is being used when 3x+123x+12 is rewritten as 3(x+4)3(x+4)?

  1. A

    Associative property

  2. B

    Identity property

  3. C

    Inverse property

  4. D

    Distributive property

17
Written response
1 point

Evaluate 3x2−4x+13x^2-4x+1 when x=−2x=-2. Enter the numerical value only.

18
Choose one
1 point

Factor 12x3+18x212x^3+18x^2 by taking out the greatest common factor.

  1. A

    6x2(2x+3)6x^2(2x+3)

  2. B

    6x(2x2+3x)6x(2x^2+3x)

  3. C

    3x2(4x+6)3x^2(4x+6)

  4. D

    12x2(x+18)12x^2(x+18)

19
Written response
1 point

Which factoring method should you use first to factor x3+3x2+2x+6x^3+3x^2+2x+6?

20
Fill in the blank
1 point

Complete the factorization and identify the pattern: x2+10x+25=x^2+10x+25=. This expression is a .