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The factor theorem states that for any polynomial function f(x), if f(a) = 0, then (x-a) is a factor of f(x).

Let f(x) = x3-2x2-8x-5. If (x+1) is a factor, then f(-1) = 0. (x+1 = x - (-1))

Input x = -1 into f: (-1)3-2(-1)2-8(-1)-5

f(-1) = -1 -2 + 8 - 5

f(-1) = 0.

Since f(-1) = 0, (x+1) is a factor of x3-2x2-8x-5.

Q.E.D.

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Q: Describe how the Factor Theorem can be used to determine whether x plus 1 is a factor of x3-2x2-8x-5?
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