Factor 5x^2-45x+90

$5 x^{2} - 45 x + 90$

Step 1

Factor $5$ out of $5 x^{2} - 45 x + 90$ .

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

$5 (x^{2}) - 45 x + 90$

Factor $5$ out of $- 45 x$ .

$5 (x^{2}) + 5 (- 9 x) + 90$

Factor $5$ out of $90$ .

$5 x^{2} + 5 (- 9 x) + 5 \cdot 18$

Factor $5$ out of $5 x^{2} + 5 (- 9 x)$ .

$5 (x^{2} - 9 x) + 5 \cdot 18$

Factor $5$ out of $5 (x^{2} - 9 x) + 5 \cdot 18$ .

$5 (x^{2} - 9 x + 18)$

Step 2

Factor.

Factor $x^{2} - 9 x + 18$ 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 $18$ and whose sum is $- 9$ .

$- 6, - 3$

Write the factored form using these integers.

$5 ((x - 6) (x - 3))$

Remove unnecessary parentheses.

$5 (x - 6) (x - 3)$

Factor 5x^2-45x+90

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