Factor 4y^2+7y-2

$4 y^{2} + 7 y - 2$

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 $a \cdot c = 4 \cdot - 2 = - 8$ and whose sum is $b = 7$ .

Factor $7$ out of $7 y$ .

$4 y^{2} + 7 (y) - 2$

Rewrite $7$ as $- 1$ plus $8$

$4 y^{2} + (- 1 + 8) y - 2$

Apply the distributive property.

$4 y^{2} - 1 y + 8 y - 2$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 y^{2} - 1 y) + 8 y - 2$

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

$y (4 y - 1) + 2 (4 y - 1)$

Step 3

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

$(4 y - 1) (y + 2)$

Factor 4y^2+7y-2

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