Factor 4x^2+7x-15

$4 x^{2} + 7 x - 15$

Step 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 $a \cdot c = 4 \cdot - 15 = - 60$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$4 x^{2} + 7 (x) - 15$

Rewrite $7$ as $- 5$ plus $12$

$4 x^{2} + (- 5 + 12) x - 15$

Apply the distributive property.

$4 x^{2} - 5 x + 12 x - 15$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 5 x) + 12 x - 15$

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

$x (4 x - 5) + 3 (4 x - 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 5$ .

$(4 x - 5) (x + 3)$

Factor 4x^2+7x-15

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