Factor 8x^2-18x-35

$8 x^{2} - 18 x - 35$

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 $a \cdot c = 8 \cdot - 35 = - 280$ and whose sum is $b = - 18$ .

Factor $- 18$ out of $- 18 x$ .

$8 x^{2} - 18 (x) - 35$

Rewrite $- 18$ as $10$ plus $- 28$

$8 x^{2} + (10 - 28) x - 35$

Apply the distributive property.

$8 x^{2} + 10 x - 28 x - 35$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 10 x) - 28 x - 35$

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

$2 x (4 x + 5) - 7 (4 x + 5)$

Step 3

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

$(4 x + 5) (2 x - 7)$

Factor 8x^2-18x-35

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