Algebra Examples

$6 y^{2} - 21 y - 45$

Step 1

Factor out the GCF of $3$ from $6 y^{2} - 21 y - 45$ .

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Step 1.1

Factor out the GCF of $3$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $3$ from the expression $6 y^{2}$ .

$3 (2 y^{2}) - 21 y - 45$

Step 1.1.2

Factor out the GCF of $3$ from the expression $- 21 y$ .

$3 (2 y^{2}) + 3 (- 7 y) - 45$

Step 1.1.3

Factor out the GCF of $3$ from the expression $- 45$ .

$3 (2 y^{2}) + 3 (- 7 y) + 3 (- 15)$

Step 1.2

Since all the terms share a common factor of $3$ , it can be factored out of each term.

$3 (2 y^{2} - 7 y - 15)$

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 $a \cdot c = 2 \cdot - 15 = - 30$ and whose sum is $b = - 7$ .

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Step 2.1.1

Factor $- 7$ out of $- 7 y$ .

$3 (2 y^{2} - 7 y - 15)$

Step 2.1.2

Rewrite $- 7$ as $3$ plus $- 10$

$3 (2 y^{2} + (3 - 10) y - 15)$

Step 2.1.3

Apply the distributive property.

$3 (2 y^{2} + 3 y - 10 y - 15)$

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.

$3 ((2 y^{2} + 3 y) - 10 y - 15)$

Step 2.2.2

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

$3 (y (2 y + 3) - 5 (2 y + 3))$

Step 2.3

Factor the polynomial by factoring out the greatest common factor, $2 y + 3$ .

$3 ((2 y + 3) (y - 5))$