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How can the Factor Theorem be used to determine if \(x-1\) is a factor of \(x^{3}-2 x^{2}-11 x+12 ?\)

Short Answer

Expert verified
\(x-1\) is a factor of \(x^{3}-2x^{2}-11x+12\).

Step by step solution

01

Substitute

Substitute x=1 into the polynomial: \(1^{3}-2(1)^{2}-11(1)+12\).
02

Simplify

Simplify the expression after substitution: \(1-2-11+12=0\).
03

Check the Result

The result is 0 which implies that \(x-1\) is indeed a factor of \(x^{3}-2x^{2}-11x+12\), according to the Factor Theorem.

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