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6 July, 17:53

Show all work to solve

3x^2 - 5x - 2 = 0

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  1. 6 July, 18:10
    0
    Factor and set each factor equal to zero.

    x = 2, - 1/3

    Explanation:

    The first term is, 3x2 its coefficient is 3.

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

    The last term, "the constant", is - 2

    Step-1 : Multiply the coefficient of the first term by the constant 3 • - 2 = - 6

    Step-2 : Find two factors of - 6 whose sum equals the coefficient of the middle term, which is - 5.

    -6 + 1 = - 5 That's it

    Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 1

    3x2 - 6x + 1x - 2

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

    3x • (x-2)

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

    1 • (x-2)

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

    (3x+1) • (x-2)

    Which is the desired factorization

    Equation at the end of step 2:

    (x - 2) • (3x + 1) = 0
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