Factor c^3+9c^2+18c

$c^{3} + 9 c^{2} + 18 c$

Step 1

Factor $c$ out of $c^{3} + 9 c^{2} + 18 c$ .

Factor $c$ out of $c^{3}$ .

$c \cdot c^{2} + 9 c^{2} + 18 c$

Factor $c$ out of $9 c^{2}$ .

$c \cdot c^{2} + c (9 c) + 18 c$

Factor $c$ out of $18 c$ .

$c \cdot c^{2} + c (9 c) + c \cdot 18$

Factor $c$ out of $c \cdot c^{2} + c (9 c)$ .

$c (c^{2} + 9 c) + c \cdot 18$

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

$c (c^{2} + 9 c + 18)$

Step 2

Factor.

Factor $c^{2} + 9 c + 18$ 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 $9$ .

$3, 6$

Write the factored form using these integers.

$c ((c + 3) (c + 6))$

Remove unnecessary parentheses.

$c (c + 3) (c + 6)$

Factor c^3+9c^2+18c

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