Prove that ( $x - 2$ ) is a factor of $p (x) = x^{3} - 2 x^{2}$ .

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Solution

Factor theorem:
If $p (c) = 0$ , then $x - c$ is a factor of the polynomial $p (x)$

Here,
$p (x) = x^{3} - 2 x^{2}$

Now, $p (2) = 2^{3} - (2) 2^{2}$
$= 8 - 8 = 0$

So, $(x - 2)$ is a factor of the polynomial $p (x)$ (proved)

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Prove that (x−2) is a factor of p(x)=x3−2x2.

Factor theorem:If p(c)=0 , then x−c is a factor of the polynomial p(x)Here,p(x)=x3−2x2Now, p(2)=23−(2)22 =8−8=0So, (x−2) is a factor of the polynomial p(x) (proved)

Prove that ( $x - 2$ ) is a factor of $p (x) = x^{3} - 2 x^{2}$ .

Factor theorem:
If $p (c) = 0$ , then $x - c$ is a factor of the polynomial $p (x)$

Here,
$p (x) = x^{3} - 2 x^{2}$

Now, $p (2) = 2^{3} - (2) 2^{2}$
$= 8 - 8 = 0$

So, $(x - 2)$ is a factor of the polynomial $p (x)$ (proved)