Factor 20x^2+21x-5

$20 x^{2} + 21 x - 5$

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 $a \cdot c = 20 \cdot - 5 = - 100$ and whose sum is $b = 21$ .

Factor $21$ out of $21 x$ .

$20 x^{2} + 21 (x) - 5$

Rewrite $21$ as $- 4$ plus $25$

$20 x^{2} + (- 4 + 25) x - 5$

Apply the distributive property.

$20 x^{2} - 4 x + 25 x - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(20 x^{2} - 4 x) + 25 x - 5$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x - 1$ .

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

Factor 20x^2+21x-5

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