df asked in Science & MathematicsMathematics · 3 weeks ago

Algebra factoring question: Why is the answer D? I don’t understand how they got there?

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  • 3 weeks ago

    Substitute mn for p in each of the proposed answers, then look for counterexamples:

    (A)

    m + p = m + mn = m (1 + n)

    When m = 2 and n = 3, the expression is = 8, and n is not a factor of 8

    (B)

    m + n + p = m + n + mn = m + n (1 + m)

    When m = 2 and n = 3, the expression is = 11, and n is not a factor of 11

    (C)

    mp - m = nm^2 - m = m (mn - 1)

    When m = 2 and n = 3 , the expression is = 10, and n is not a factor of 10

    (D)

    mp - n = m^2n - n = n (m^2 - 1)

    n is always a factor of n (m^2 - 1) except when m = 1

    (E)

    np - m = mn^2 - m = m (n^2 -1)

    When m = 2 and n = 3, the expression is = 16, and n is not a factor of 16

    So the answer closest to correct is (D).

    [(D) could be made entirely correct by adding the requirement: m > n ]

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