Factor 8x^2-10x-25

$8 x^{2} - 10 x - 25$

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 $a \cdot c = 8 \cdot - 25 = - 200$ and whose sum is $b = - 10$ .

Factor $- 10$ out of $- 10 x$ .

$8 x^{2} - 10 (x) - 25$

Rewrite $- 10$ as $10$ plus $- 20$

$8 x^{2} + (10 - 20) x - 25$

Apply the distributive property.

$8 x^{2} + 10 x - 20 x - 25$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 10 x) - 20 x - 25$

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

$2 x (4 x + 5) - 5 (4 x + 5)$

Step 3

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

$(4 x + 5) (2 x - 5)$

Factor 8x^2-10x-25

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