Factor 8y^2-26y+18

$8 y^{2} - 26 y + 18$

Step 1

Factor $2$ out of $8 y^{2} - 26 y + 18$ .

Factor $2$ out of $8 y^{2}$ .

$2 (4 y^{2}) - 26 y + 18$

Factor $2$ out of $- 26 y$ .

$2 (4 y^{2}) + 2 (- 13 y) + 18$

Factor $2$ out of $18$ .

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

Factor $2$ out of $2 (4 y^{2}) + 2 (- 13 y)$ .

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

Factor $2$ out of $2 (4 y^{2} - 13 y) + 2 (9)$ .

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

Step 2

Factor.

Factor by grouping.

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 $- 13 y$ .

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

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

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

Apply the distributive property.

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

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 (4 y (y - 1) - 9 (y - 1))$

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

$2 ((y - 1) (4 y - 9))$

Remove unnecessary parentheses.

$2 (y - 1) (4 y - 9)$

Factor 8y^2-26y+18

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