Find whether $x+2$ is the factor of $x^2 - 4$
Given :
$f(x) = x^2 - 4$
$g(x) = x+2 = x-(-2)$
To do :
We have to check whether $x+2$ is the factor of $x^2 - 4$.
Solution :
According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, $(x-a)$ is a factor of f(x), if $f(a)=0$.
Therefore,
g(x) is a factor of f(x) if $f(-2) = 0$.
$f(-2) = (-2)^2-4$
$= 4-4$
= 0
$f(-2)$ is equal to zero.
Therefore,$x+2$ is a factor of$x^2 - 4$.
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