Factor 5x^2+8x-4

$5 x^{2} + 8 x - 4$

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 $a \cdot c = 5 \cdot - 4 = - 20$ and whose sum is $b = 8$ .

Factor $8$ out of $8 x$ .

$5 x^{2} + 8 (x) - 4$

Rewrite $8$ as $- 2$ plus $10$

$5 x^{2} + (- 2 + 10) x - 4$

Apply the distributive property.

$5 x^{2} - 2 x + 10 x - 4$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} - 2 x) + 10 x - 4$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 2$ .

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

Factor 5x^2+8x-4

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