Factor 4x^2-14x-30

$4 x^{2} - 14 x - 30$

Step 1

Factor $2$ out of $4 x^{2} - 14 x - 30$ .

Factor $2$ out of $4 x^{2}$ .

$2 (2 x^{2}) - 14 x - 30$

Factor $2$ out of $- 14 x$ .

$2 (2 x^{2}) + 2 (- 7 x) - 30$

Factor $2$ out of $- 30$ .

$2 (2 x^{2}) + 2 (- 7 x) + 2 (- 15)$

Factor $2$ out of $2 (2 x^{2}) + 2 (- 7 x)$ .

$2 (2 x^{2} - 7 x) + 2 (- 15)$

Factor $2$ out of $2 (2 x^{2} - 7 x) + 2 (- 15)$ .

$2 (2 x^{2} - 7 x - 15)$

Step 2

Factor.

Factor by grouping.

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 $b = - 7$ .

Factor $- 7$ out of $- 7 x$ .

$2 (2 x^{2} - 7 (x) - 15)$

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

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

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

Remove unnecessary parentheses.

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

Factor 4x^2-14x-30

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