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9 October, 13:43

What are the factors of 2x^2 + 5x - 12?

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  1. 9 October, 15:51
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    (2x - 3) • (x + 4)

    Step-by-step explanation:

    Step 1:

    Equation at step 1:

    (2x2 + 5x) - 12

    Step 2:

    Trying to factor by splitting the middle term

    2.1 Factoring 2x2+5x-12

    The first term is, 2x2 its coefficient is 2.

    The middle term is, + 5x its coefficient is 5.

    The last term, "the constant", is - 12

    Step-1 : Multiply the coefficient of the first term by the constant 2 • - 12 = - 24

    Step-2 : Find two factors of - 24 whose sum equals the coefficient of the middle term, which is 5.

    -24 + 1 = - 23

    -12 + 2 = - 10

    -8 + 3 = - 5

    -6 + 4 = - 2

    -4 + 6 = 2

    -3 + 8 = 5

    Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 3 and 8

    2x2 - 3x + 8x - 12

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

    x • (2x-3)

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

    4 • (2x-3)

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

    (x+4) • (2x-3)

    Which is the desired factorization
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