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# What does the factor theorem mean?

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Tony B Share
Jun 19, 2018

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#### Explanation:

Suppose you have an equation. For example: $y = {x}^{2} - x - 12$

In this case if we set $y = 0$ and substitute $4$ for $x$ then we have: $y = {\left(4\right)}^{2} - \left(4\right) - 12 = 16 - 4 - 12 = 0$

So if the equation equals 0 $\to f \left(x\right) = 0$

and by substituting $x = 4 \to f \left(4\right)$ we get the answer $f \left(4\right) = 0$

then by using $\left(x - 4\right) \left(\text{something else") ->0("something else}\right) = 0$
So $\left(x - 4\right)$ is a factor of $f \left(x\right)$

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Jun 19, 2018

According to Factor Theorem: If $x = a$ satisfies the polynomial $P \left(x\right)$ i.e. if $x = a$ is a root of the polynomial equation $P \left(x\right) = 0$ then $\left(x - a\right)$ will be a factor of polynomial $P \left(x\right)$

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