Factor 4y^2-13y+9

$4 y^{2} - 13 y + 9$

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 $a \cdot c = 4 \cdot 9 = 36$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 y$ .

$4 y^{2} - 13 (y) + 9$

Rewrite $- 13$ as $- 4$ plus $- 9$

$4 y^{2} + (- 4 - 9) y + 9$

Apply the distributive property.

$4 y^{2} - 4 y - 9 y + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 y^{2} - 4 y) - 9 y + 9$

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

$4 y (y - 1) - 9 (y - 1)$

Step 3

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

$(y - 1) (4 y - 9)$

Factor 4y^2-13y+9

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