Factor by Grouping 5x^2+15x+11.25

$5 x^{2} + 15 x + 11.25$

Step 1

Factor $1.25$ out of $5 x^{2} + 15 x + 11.25$ .

Factor $1.25$ out of $5 x^{2}$ .

$1.25 (4 x^{2}) + 15 x + 11.25$

Factor $1.25$ out of $15 x$ .

$1.25 (4 x^{2}) + 1.25 (12 x) + 11.25$

Factor $1.25$ out of $11.25$ .

$1.25 (4 x^{2}) + 1.25 (12 x) + 1.25 (9)$

Factor $1.25$ out of $1.25 (4 x^{2}) + 1.25 (12 x)$ .

$1.25 (4 x^{2} + 12 x) + 1.25 (9)$

Factor $1.25$ out of $1.25 (4 x^{2} + 12 x) + 1.25 (9)$ .

$1.25 (4 x^{2} + 12 x + 9)$

Step 2

Factor using the perfect square rule.

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$1.25 ({(2 x)}^{2} + 12 x + 9)$

Rewrite $9$ as $3^{2}$ .

$1.25 ({(2 x)}^{2} + 12 x + 3^{2})$

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

$12 x = 2 \cdot (2 x) \cdot 3$

Rewrite the polynomial.

$1.25 ({(2 x)}^{2} + 2 \cdot (2 x) \cdot 3 + 3^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 x$ and $b = 3$ .

$1.25 {(2 x + 3)}^{2}$