Pre-Algebra Examples

$36 x^{2} + 30 x - 36$

Step 1

Factor out the GCF of $6$ from $36 x^{2} + 30 x - 36$ .

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Step 1.1

Factor out the GCF of $6$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $6$ from the expression $36 x^{2}$ .

$6 (6 x^{2}) + 30 x - 36$

Step 1.1.2

Factor out the GCF of $6$ from the expression $30 x$ .

$6 (6 x^{2}) + 6 (5 x) - 36$

Step 1.1.3

Factor out the GCF of $6$ from the expression $- 36$ .

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

Step 1.2

Since all the terms share a common factor of $6$ , it can be factored out of each term.

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

Step 2

Factor by grouping.

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Step 2.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 6 \cdot - 6 = - 36$ and whose sum is $b = 5$ .

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Step 2.1.1

Factor $5$ out of $5 x$ .

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

Step 2.1.2

Rewrite $5$ as $- 4$ plus $9$

$6 (6 x^{2} + (- 4 + 9) x - 6)$

Step 2.1.3

Apply the distributive property.

$6 (6 x^{2} - 4 x + 9 x - 6)$

Step 2.2

Factor out the greatest common factor from each group.

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Step 2.2.1

Group the first two terms and the last two terms.

$6 ((6 x^{2} - 4 x) + 9 x - 6)$

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

$6 (2 x (3 x - 2) + 3 (3 x - 2))$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $3 x - 2$ .

$6 ((3 x - 2) (2 x + 3))$