true or false by the factor theorem if f(k) = 0 for a polynomial f(x) then the polynomial has a factor (x+k). If false correct the underline words, the polynomial has a factor (x+k)

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embizze | High School Teacher | (Level 2) Educator Emeritus

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If f(k)=0 for some polynomial, then by the factor theorem (x-k) is a factor, not (x+k).

So the answer is false.

For example, for the polynomial `f(x)=x^2-2x+1 ` we have f(1)=0, but (x+1) is not a factor since `x^2-2x+1=(x-1)^2 ` ; the only factor is (x-1).


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