Question

Use the factor theorem to determine if the binomial is a factor of the the polynomial

Answer 1

9514 1404 393

Answer:

1. yes
2. no
3. no

Explanation:

1. f(2) = 2^5 -32 = 0 . . . . (x -2) is a factor

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2. f(5)) = (x -16)x +34 = (-11)(5) +34 = -21 . . . . (x -5) is not a factor

We also note that 5 is not a factor of 34, so cannot be a root of f(x).

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3. f(2) = ((x^2+4)x^2 +2)x -16 = ((4 +4)(4) +2)2 -16 = 34(2) -16 = 52

(x -2) is not a factor