Factor 8x^2+18x-5

$8 x^{2} + 18 x - 5$

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 $a \cdot c = 8 \cdot - 5 = - 40$ and whose sum is $b = 18$ .

Factor $18$ out of $18 x$ .

$8 x^{2} + 18 (x) - 5$

Rewrite $18$ as $- 2$ plus $20$

$8 x^{2} + (- 2 + 20) x - 5$

Apply the distributive property.

$8 x^{2} - 2 x + 20 x - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} - 2 x) + 20 x - 5$

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

$2 x (4 x - 1) + 5 (4 x - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x - 1$ .

$(4 x - 1) (2 x + 5)$

Factor 8x^2+18x-5

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