Chapter 12: Mock Test

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  • 1/12 Questions

    Problem solving If 35 = x^2 + 3x is the number of bottles you drink a day. Find all possible values for x.                 2

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About This Quiz

Chapter 12: Mock Test assesses understanding of polynomial operations, including factoring, identifying square differences, and recognizing binomial factors. This quiz is designed to enhance critical thinking and problem-solving skills in algebra.

Chapter 12: Mock Test - Quiz

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  • 2. 

    Polynomials can either be a sum or difference of terms; factoring will not affect this operation.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    Factoring transforms a polynomial to its products, thus changing the operation to multiplication.
    Ex: x^2 + 2x + 1 [a sum] = (x+1)(x+1) [the parenthesis means multiply]

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  • 3. 

    Find the missing term: -5k + 10m – 15n = ___(k – 2m + 3n)

    • -5

    • 5

    • -5k

    • Greatest Common Factor

    Correct Answer
    A. -5
    Explanation
    This is factoring by grouping

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  • 4. 

    Find the missing term: a(c + d) – b(c + d) = ______ (c + d)

    • (a +d)

    • (a - d)

    • (d + a)

    • (d – a)

    Correct Answer
    A. (a - d)
    Explanation
    This is again factoring by grouping.

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  • 5. 

    If x^2 – 1 = (x + 1)(x – 1); then x^2 + 1 = (x + 1)(x + 1)

    • True

    • False

    Correct Answer
    A. False
    Explanation
    x^2 – 1 is a difference of two squares, that’s why it can be factored. But x^2 + 1 is a sum… we can not factor a sum of two squares.

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  • 6. 

    Complete the missing terms: X^2 + ___ + 36 = (x + ___)(x+ 6)

    • 6x and 6

    • 9x and 6

    • 6x and 9

    • 12x and 6

    Correct Answer
    A. 12x and 6
    Explanation
    This is a perfect square trinomial.

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  • 7. 

    Complete the equation: 4x^2 – ___ = (2x + 3)(2x - ___)

    • 6 and 2

    • 2 and 6

    • 9 and 3

    • 3 and 9

    Correct Answer
    A. 9 and 3
    Explanation
    This is a difference of two squares pattern.

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  • 8. 

    If 2 is common in ‘2xy + 2xz’, then the GCF of the binomial is 2 and its factors are 2 and xy + xz.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    The Greatest Common Factor (GCF) is the biggest value, or number of common factors, a polynomial can have. In this light, notice that 2x is common on both terms.
    ‘2xy + 2xz’
    This means that 2x is the GCF. And that the factored forms is 2x and y + z.

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  • 9. 

    2x^2 – 16 is a difference of two squares.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    To answer this check each term if it is a perfect square.
    Is – 16 a perfect square? (yes!)
    Is 2x^2 a perfect square? (NO, because the coefficient is 2. and 2 is not a perfect square.)

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  • 10. 

    4 is the missing term in x^2 -___x + 3

    • True

    • False

    Correct Answer
    A. True
    Explanation
    Check out the sign of the last term.
    It’s positive, right?
    if it is, it means add the factors of three or find the sum of OI in FOIL. On the other hand, if it’s ‘–‘ it means subtract or find the difference of OI in FOIL.

    Thus, the missing terms is the sum of the factors of 3... or just simply the sum of 3 and 1, which is 4.

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  • 11. 

    X^2 – 4 is a square of the difference.

    • True

    • False

    Correct Answer
    A. False
    Explanation
    Pay careful attention on the terminologies presented in chapter 12, for it can not be interchanged. Because changing it would change its meaning. This is true to the following terms:
    Zero Product Property
    Difference of two Squares
    Sum and Difference of two Cubes
    and
    Perfect square Trinomials

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  • 12. 

    Find the missing terms: (2x - ___)(3x + ___) = ___ - x – 35

    • 5, 7 and 5x^2

    • 7, 5 and 5x^2

    • 7, 5 and 6x^2

    • 5, 7 and 6x^2

    Correct Answer
    A. 5, 7 and 6x^2
    Explanation
    This is factoring complex trinomials.

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  • Jul 17, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 16, 2010
    Quiz Created by
    Marvinjaybaclay
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