How do I use the factor theorem to prove $x-2$ must be a factor of $2x^3-x^2-7x+2$ ?

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How do I use the factor theorem to prove $x-2$ must be a factor of $2x^3-x^2-7x+2$ ?

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Answer 1 · 2018-03-17T10:43:40

$"see explanation"$

Explanation:

$"for a polynomial "f(x)$

$• " if "f(a)=0" then "(x-a)" is a factor of "f(x)$

$"substitute "x=2 " into the polynomial"$

$rArr2(2)^3-(2)^2-7(2)+2=0$

$rArr(x-2)" is a factor of "2x^3-x^2-7x+2$

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How do I use the factor theorem to prove $x-2$ must be a factor of $2x^3-x^2-7x+2$ ?

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How do I use the factor theorem to prove x-2x-2 must be a factor of 2x^3-x^2-7x+22x^3-x^2-7x+2?

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How do I use the factor theorem to prove $x-2$ must be a factor of $2x^3-x^2-7x+2$ ?