Factor 5x^2+40x+75

$5 x^{2} + 40 x + 75$

Step 1

Factor $5$ out of $5 x^{2} + 40 x + 75$ .

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

$5 (x^{2}) + 40 x + 75$

Factor $5$ out of $40 x$ .

$5 (x^{2}) + 5 (8 x) + 75$

Factor $5$ out of $75$ .

$5 x^{2} + 5 (8 x) + 5 \cdot 15$

Factor $5$ out of $5 x^{2} + 5 (8 x)$ .

$5 (x^{2} + 8 x) + 5 \cdot 15$

Factor $5$ out of $5 (x^{2} + 8 x) + 5 \cdot 15$ .

$5 (x^{2} + 8 x + 15)$

Step 2

Factor.

Factor $x^{2} + 8 x + 15$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $15$ and whose sum is $8$ .

$3, 5$

Write the factored form using these integers.

$5 ((x + 3) (x + 5))$

Remove unnecessary parentheses.

$5 (x + 3) (x + 5)$

Factor 5x^2+40x+75

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