Factor 4y^2-y-3

$4 y^{2} - y - 3$

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 $a \cdot c = 4 \cdot - 3 = - 12$ and whose sum is $b = - 1$ .

Factor $- 1$ out of $- y$ .

$4 y^{2} - (y) - 3$

Rewrite $- 1$ as $3$ plus $- 4$

$4 y^{2} + (3 - 4) y - 3$

Apply the distributive property.

$4 y^{2} + 3 y - 4 y - 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 y^{2} + 3 y) - 4 y - 3$

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

$y (4 y + 3) - (4 y + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 y + 3$ .

$(4 y + 3) (y - 1)$

Factor 4y^2-y-3

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