Factor 9y^2-34y+25

$9 y^{2} - 34 y + 25$

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 $a \cdot c = 9 \cdot 25 = 225$ and whose sum is $b = - 34$ .

Factor $- 34$ out of $- 34 y$ .

$9 y^{2} - 34 (y) + 25$

Rewrite $- 34$ as $- 9$ plus $- 25$

$9 y^{2} + (- 9 - 25) y + 25$

Apply the distributive property.

$9 y^{2} - 9 y - 25 y + 25$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(9 y^{2} - 9 y) - 25 y + 25$

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

$9 y (y - 1) - 25 (y - 1)$

Step 3

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

$(y - 1) (9 y - 25)$

Factor 9y^2-34y+25

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