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7 June, 19:19

Which solution set represents the solution to x^2+10x-56=0 A. (4,14) B. (4,-14) C. (-4,14) D. (-4,-14)

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  1. 7 June, 20:01
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    C

    Step-by-step explanation:

    Step-1 : Multiply the coefficient of the first term by the constant 1 • - 56 = - 56

    Step-2 : Find two factors of - 56 whose sum equals the coefficient of the middle term, which is - 10.

    -56 + 1 = - 55

    -28 + 2 = - 26

    -14 + 4 = - 10 That's it

    Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 14 and 4

    x2 - 14x + 4x - 56

    Step-4 : Add up the first 2 terms, pulling out like factors:

    x • (x-14)

    Add up the last 2 terms, pulling out common factors:

    4 • (x-14)

    Step-5 : Add up the four terms of step 4:

    (x+4) • (x-14)

    Which is the desired factorization

    Equation at the end of step 1:

    (x + 4) • (x - 14) = 0
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