Factor 10y^2-26y+16

$10 y^{2} - 26 y + 16$

Step 1

Factor $2$ out of $10 y^{2} - 26 y + 16$ .

Factor $2$ out of $10 y^{2}$ .

$2 (5 y^{2}) - 26 y + 16$

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

$2 (5 y^{2}) + 2 (- 13 y) + 16$

Factor $2$ out of $16$ .

$2 (5 y^{2}) + 2 (- 13 y) + 2 (8)$

Factor $2$ out of $2 (5 y^{2}) + 2 (- 13 y)$ .

$2 (5 y^{2} - 13 y) + 2 (8)$

Factor $2$ out of $2 (5 y^{2} - 13 y) + 2 (8)$ .

$2 (5 y^{2} - 13 y + 8)$

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 $a \cdot c = 5 \cdot 8 = 40$ and whose sum is $b = - 13$ .

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

$2 (5 y^{2} - 13 (y) + 8)$

Rewrite $- 13$ as $- 5$ plus $- 8$

$2 (5 y^{2} + (- 5 - 8) y + 8)$

Apply the distributive property.

$2 (5 y^{2} - 5 y - 8 y + 8)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$2 ((5 y^{2} - 5 y) - 8 y + 8)$

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

$2 (5 y (y - 1) - 8 (y - 1))$

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

$2 ((y - 1) (5 y - 8))$

Remove unnecessary parentheses.

$2 (y - 1) (5 y - 8)$

Factor 10y^2-26y+16

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