Factor 3x^2+24x+48

$3 x^{2} + 24 x + 48$

Factor $3$ out of $3 x^{2} + 24 x + 48$ .

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) + 24 x + 48$

Factor $3$ out of $24 x$ .

$3 (x^{2}) + 3 (8 x) + 48$

Factor $3$ out of $48$ .

$3 x^{2} + 3 (8 x) + 3 \cdot 16$

Factor $3$ out of $3 x^{2} + 3 (8 x)$ .

$3 (x^{2} + 8 x) + 3 \cdot 16$

Factor $3$ out of $3 (x^{2} + 8 x) + 3 \cdot 16$ .

$3 (x^{2} + 8 x + 16)$

Factor using the perfect square rule.

Rewrite $16$ as $4^{2}$ .

$3 (x^{2} + 8 x + 4^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 x = 2 \cdot x \cdot 4$

Rewrite the polynomial.

$3 (x^{2} + 2 \cdot x \cdot 4 + 4^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 4$ .

$3 {(x + 4)}^{2}$