Algebra Examples

$2 x^{3} + 10 x^{2} + 12 x$

Step 1

Factor out the GCF of $2 x$ from $2 x^{3} + 10 x^{2} + 12 x$ .

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Step 1.1

Factor out the GCF of $2 x$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $2 x$ from the expression $2 x^{3}$ .

$2 x (x^{2}) + 10 x^{2} + 12 x$

Step 1.1.2

Factor out the GCF of $2 x$ from the expression $10 x^{2}$ .

$2 x (x^{2}) + 2 x (5 x) + 12 x$

Step 1.1.3

Factor out the GCF of $2 x$ from the expression $12 x$ .

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

Step 1.2

Since all the terms share a common factor of $2 x$ , it can be factored out of each term.

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

Step 2

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

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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.

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