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25 November, 13:19

What is the factor of k2 + k - 42

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Answers (1)
  1. 25 November, 13:30
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    (k + 7) • (k - 6)

    Step-by-step explanation:

    Final result:

    (k + 7) • (k - 6)

    Reformatting the input:

    Changes made to your input should not affect the solution:

    (1) : "k2" was replaced by "k^2".

    Step by step solution:

    Step 1:

    Trying to factor by splitting the middle term

    1.1 Factoring k2+k-42

    The first term is, k2 its coefficient is 1.

    The middle term is, + k its coefficient is 1.

    The last term, "the constant", is - 42

    Step-1 : Multiply the coefficient of the first term by the constant 1 • - 42 = - 42

    Step-2 : Find two factors of - 42 whose sum equals the coefficient of the middle term, which is 1.

    -42 + 1 = - 41

    -21 + 2 = - 19

    -14 + 3 = - 11

    -7 + 6 = - 1

    -6 + 7 = 1 That's it

    Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 7

    k2 - 6k + 7k - 42

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

    k • (k-6)

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

    7 • (k-6)

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

    (k+7) • (k-6)

    Which is the desired factorization

    Final result:

    (k + 7) • (k - 6)
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