How do you use the factor theorem to determine whether x+3 is a factor of $2x^3 + x^2 – 13x + 6$ ?

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How do you use the factor theorem to determine whether x+3 is a factor of $2x^3 + x^2 – 13x + 6$ ?

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Answer 1 · 2016-01-06T16:30:07

For $f(x)=2x^3+x^2-13x+6$
If $(x+3)$ is a factor, $x=-3$ should be a root.
So for $x=-3$ to be a root, $f(-3)=0$
If $f(-3)!=0$ , $(x+3)$ is not a factor.

Explanation:

Factor theorem basically boils down to testing potential roots in the equation.

So for some equation $f(x)$

A root is an $x$ value which satisfies $f(x)=0$

So if a factor of $f(x)$ is $(x-a)$ ,
$x=a$ is a root of $f(x)$ .

So for your case,
$f(x)=2x^3+x^2-13x+6$ ,
we want to see if $(x+3)$ is a factor.
So we test $x=-3$

$f(-3)=-54+9+39+6=0$
$f(-3)=0$ so $x=-3$ is a root.
Therefore $(x+3)$ is indeed a factor.

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How do you use the factor theorem to determine whether x+3 is a factor of $2x^3 + x^2 – 13x + 6$ ?

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How do you use the factor theorem to determine whether x+3 is a factor of $2x^3 + x^2 – 13x + 6$ ?