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25 January, 16:51

Two students, Ann and Max, factored the trinomial '3x^2 - 24x-27'. Ann factored it as 3 (x+1) (x-9) and Max factored it as (3x+3) (x-9). Indicate which student factored the trinomial completely and which student did not, and explain why.

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  1. 25 January, 17:10
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    Let's start studying case by case:

    Ann:

    3x ^ 2 - 24x-27

    3 (x ^ 2 - 8x-9)

    3 (x + 1) (x-9)

    Note:

    (1) * ( - 9) = - 9

    (1) + ( - 9) = - 8

    check:

    3 (x ^ 2-9x + x-9)

    3 (x ^ 2-8x-9)

    3x ^ 2-24x-27

    She did it correctly.

    Max

    3x ^ 2 - 24x-27

    (3x + 3) (x-9)

    note:

    (3) * ( - 9) = - 27

    (3) + ( - 9) = - 6 (incorrect: the result must be - 24)
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