Factor 10y^2+17y-20

$10 y^{2} + 17 y - 20$

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 $a \cdot c = 10 \cdot - 20 = - 200$ and whose sum is $b = 17$ .

Factor $17$ out of $17 y$ .

$10 y^{2} + 17 (y) - 20$

Rewrite $17$ as $- 8$ plus $25$

$10 y^{2} + (- 8 + 25) y - 20$

Apply the distributive property.

$10 y^{2} - 8 y + 25 y - 20$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 y^{2} - 8 y) + 25 y - 20$

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

$2 y (5 y - 4) + 5 (5 y - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 y - 4$ .

$(5 y - 4) (2 y + 5)$

Factor 10y^2+17y-20

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