Factor 5y^2+4y-1

$5 y^{2} + 4 y - 1$

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 $a \cdot c = 5 \cdot - 1 = - 5$ and whose sum is $b = 4$ .

Factor $4$ out of $4 y$ .

$5 y^{2} + 4 (y) - 1$

Rewrite $4$ as $- 1$ plus $5$

$5 y^{2} + (- 1 + 5) y - 1$

Apply the distributive property.

$5 y^{2} - 1 y + 5 y - 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 y^{2} - 1 y) + 5 y - 1$

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

$y (5 y - 1) + 1 (5 y - 1)$

Step 3

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

$(5 y - 1) (y + 1)$

Factor 5y^2+4y-1

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