Factor 4h^2+8h-5

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

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

Factor $8$ out of $8 h$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 h (2 h - 1) + 5 (2 h - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 h - 1$ .

$(2 h - 1) (2 h + 5)$

Factor 4h^2+8h-5

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