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31 December, 11:28

Is the binomial a factor of the polynomial function? f (x) = x3+2x2-16x-32

Select Yes or No for each binomial.

(x-2)

(x+2)

(x-4)

(x+4)

(x+6)

+2
Answers (1)
  1. 31 December, 12:35
    0
    Since it is x^3 cubed it has 3 maximum roots

    by the zero multiplication property of function

    if you plug find a root then you can deduce it is a factor in other words if f (x) = (x-a) (x-b)

    then f (a) = 0 and f (b) = 0

    so

    f (2) = 8+8-32-32 = - 48 therefore it is not a factor

    f (-2) = - 8+8+32-32=0 hence it is a factor

    f (4) = 64+32-64-32=0 it is a factor

    f (-4) = - 64+32+64-32=0 it is a factor

    f (-6) it is not a factor via the fundmental therom of algebra

    f (x) = (x+2) (x-4) (x+4)

    = (x^2-16) (x+2) = x^3+2x^2-16x-32 which checks our work
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