Question

Factorize the expression and divide them as directed:
$(3x^2-48)÷(x-4)$

Answer 1

Step 1: Factorize the expression

$3x^2-48$

By taking 3 common, we get:

$=3[x^2-16]$

$=3[x^2-4^2]$

$=3(x+4)(x-4)[\because a^2-b^2=(a+b)(a-b)]$

Step 2: Perform division of given expression

$\frac{3x^2-48}{x-4}=\frac{3(x+4)(x-4)}{x-4}$

$=3(x+4)$

$\therefore (3x^2-48)÷(x-4)=3(x+4).$