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11 October, 23:31

Is the binomial a factor of the polynomial function? f (x) = x^3+5x^2-9x-45

Select yes or no for each binomial:

(X-5)

(X+3)

(X-15)

+3
Answers (1)
  1. 12 October, 01:23
    0
    No, Yes, No

    Step-by-step explanation:

    to determine if the given binomials are factors of f (x)

    if (x - a) is a factor of a polynomial then f (a) = 0

    f (5) = 5³ + 5 (5) ² - 9 (5) - 45 = 125 + 125 - 45 - 45 = 160 ≠ 0

    ⇒ (x - 5) is not a factor

    f ( - 3) = ( - 3) ³ + 5 ( - 3) ² - 9 ( - 3) - 45 = - 27 + 45 + 27 - 45 = 0

    ⇒ (x + 3) is a factor

    f (15) = 15³ + 5 (15) ² - 9 (15) - 45 ≠ 0

    ⇒ (x - 15) is not a factor
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