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14 April, 15:43

Factor the expression. d^2-14d+49

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  1. 14 April, 15:56
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    Answer: (d - 7) ^2

    Procedure to factor:

    The expression to factor is a trinomial.

    Steps:

    1) Probe whether this is a perfect square trinomial, i. e a trinomial that can be factored as (a + b) ^2 or (a - b) ^2.:

    2) Determine if the first and the third terms of the trinomial (once it is ordered, which it is) have exact square roots:

    √ (d^2) = d

    √49 = 7

    3) Since they have exact square roots, test wether the second term of the trinomial equals twice the product of the two square roots determined:

    => 2 * (d) * (7) = 14d which is exactly the second term of the trinomial

    4) Now you can write the binomial squared using the sign of the second term. This is:

    (d - 7) ^2.

    You can prove that that is the answer by expanding the binomial squared, which must drive back to the original expression: d^2 - 2 (7) (d) + 7^2 = d^2 - 14d + 49.
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