Factorize the expression and divide them as directed:
$(3 x^{2} - 48) \div (x - 4)$

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Solution

Step 1: Factorize the expression

$3 x^{2} - 48$

By taking 3 common, we get:

$= 3 [x^{2} - 16]$

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

$= 3 (x + 4) (x - 4) [∵ a^{2} - b^{2} = (a + b) (a - b)]$

Step 2: Perform division of given expression

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

$= 3 (x + 4)$

$∴ (3 x^{2} - 48) \div (x - 4) = 3 (x + 4) .$

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