Precalculus Examples

$x^{3} + 5 x^{2} + 6 x$

Step 1

Factor out the GCF of $x$ from $x^{3} + 5 x^{2} + 6 x$ .

Tap for more steps...

Step 1.1

Factor out the GCF of $x$ from each term in the polynomial.

Tap for more steps...

Step 1.1.1

Factor out the GCF of $x$ from the expression $x^{3}$ .

$x (x^{2}) + 5 x^{2} + 6 x$

Step 1.1.2

Factor out the GCF of $x$ from the expression $5 x^{2}$ .

$x (x^{2}) + x (5 x) + 6 x$

Step 1.1.3

Factor out the GCF of $x$ from the expression $6 x$ .

$x (x^{2}) + x (5 x) + x (6)$

Step 1.2

Since all the terms share a common factor of $x$ , it can be factored out of each term.

$x (x^{2} + 5 x + 6)$

Step 2

Factor $x^{2} + 5 x + 6$ using the AC method.

Tap for more steps...

Step 2.1

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 $6$ and whose sum is $5$ .

$2, 3$

Step 2.2

Write the factored form using these integers.

$x ((x + 2) (x + 3))$