Factor 8y^2-33y+25

$8 y^{2} - 33 y + 25$

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 $a \cdot c = 8 \cdot 25 = 200$ and whose sum is $b = - 33$ .

Factor $- 33$ out of $- 33 y$ .

$8 y^{2} - 33 (y) + 25$

Rewrite $- 33$ as $- 8$ plus $- 25$

$8 y^{2} + (- 8 - 25) y + 25$

Apply the distributive property.

$8 y^{2} - 8 y - 25 y + 25$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 y^{2} - 8 y) - 25 y + 25$

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

$8 y (y - 1) - 25 (y - 1)$

Step 3

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

$(y - 1) (8 y - 25)$

Factor 8y^2-33y+25

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