Factor 24x^2-49x-40

$24 x^{2} - 49 x - 40$

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 $a \cdot c = 24 \cdot - 40 = - 960$ and whose sum is $b = - 49$ .

Factor $- 49$ out of $- 49 x$ .

$24 x^{2} - 49 (x) - 40$

Rewrite $- 49$ as $15$ plus $- 64$

$24 x^{2} + (15 - 64) x - 40$

Apply the distributive property.

$24 x^{2} + 15 x - 64 x - 40$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(24 x^{2} + 15 x) - 64 x - 40$

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

$3 x (8 x + 5) - 8 (8 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $8 x + 5$ .

$(8 x + 5) (3 x - 8)$

Factor 24x^2-49x-40

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