What does the factor theorem mean?

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What does the factor theorem mean?

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Answer 1 · 2018-06-19T20:41:57

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

Answer 2 · 2018-06-19T20:54:36

See explanation

Explanation:

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

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

So if the equation equals 0 $\to f (x) = 0$ $->f(x)=0$

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

then by using $(x - 4) (something else) \to 0 (something else) = 0$ $(x-4)("something else") ->0("something else")=0$
So $(x - 4)$ $(x-4)$ is a factor of $f (x)$ $f(x)$

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What does the factor theorem mean?

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