Use the Factor Theorem to prove x^3 – 13x – 12 is divisible by x^2 – X – 12

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Use the Factor Theorem to prove x^3 – 13x – 12 is divisible by x^2 – X – 12

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Doris 7 months 2021-07-20T21:30:35+00:00 1 Answers 8 views 0

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  1. Latifah
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    2021-07-20T21:32:24+00:00
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    Answer:

    See Below.

    Step-by-step explanation:

    We want to prove that:

    x^3-13x-12\text{ is divisible by } x^2-x-12

    We can factor the divisor:

    x^2-x-12=(x-4)(x+3)

    According to the Factor Theorem, if we have a polynomial P(x) divided by a binomial in the form of (x – a) and if P(a) = 0, then the binomial is a factor of P(x).

    Our two binomial factors our (x – 4) and (x + 3). Thus, a = 4 and a = -3.

    Evaluate the polynomial for both of these factors:

    P(4)=(4)^3-13(4)-12=0

    And:

    P(-3)=(-3)^3-13(-3)-12=0

    Since both yielded zero, the original polynomial is divisible by both (x – 4) and (x + 3) or x² – x – 12. Hence:

    x^3-13x-12\text{ is indeed divisible by } x^2-x-12

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