Question

Factorize $3x^2-27$

• A. $3(x+3)(x+3)$
• B. $3(x-3)(x-3)$
• C. $(x+3)(x-3)$
• D. $3(x+3)(x-3)$

Answer 1

The correct option is D $3(x+3)(x-3)$

Given a polynomial expression $3x^2-27$

$\underset{–}{Step1:}$

Taking $3$ common from the polynomial expression $3x^2-27$:
$3x^2-27=3(x^2-9)$


$\underset{–}{Step2:}$

$x^2$ and $9$ are the perfect squares of $x$ and $3$ respectively. Also, the terms in the bracket are of the form $a^2-b^2$.

$3(x^2-9)=3(x+3)(x-3)$ ($\because a^2-b^2=(a+b)(a-b)$)

The factorization of the polynomial $3x^2-27$ is $3(x+3)(x-3)$.
Therefore, option (d.) is the correct answer.