Factor 3x^2-27x+60

$3 x^{2} - 27 x + 60$

Step 1

Factor $3$ out of $3 x^{2} - 27 x + 60$ .

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

$3 (x^{2}) - 27 x + 60$

Factor $3$ out of $- 27 x$ .

$3 (x^{2}) + 3 (- 9 x) + 60$

Factor $3$ out of $60$ .

$3 x^{2} + 3 (- 9 x) + 3 \cdot 20$

Factor $3$ out of $3 x^{2} + 3 (- 9 x)$ .

$3 (x^{2} - 9 x) + 3 \cdot 20$

Factor $3$ out of $3 (x^{2} - 9 x) + 3 \cdot 20$ .

$3 (x^{2} - 9 x + 20)$

Step 2

Factor.

Factor $x^{2} - 9 x + 20$ 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 $20$ and whose sum is $- 9$ .

$- 5, - 4$

Write the factored form using these integers.

$3 ((x - 5) (x - 4))$

Remove unnecessary parentheses.

$3 (x - 5) (x - 4)$

Factor 3x^2-27x+60

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