Factor 3y^2-16y+16

$3 y^{2} - 16 y + 16$

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 $a \cdot c = 3 \cdot 16 = 48$ and whose sum is $b = - 16$ .

Factor $- 16$ out of $- 16 y$ .

$3 y^{2} - 16 (y) + 16$

Rewrite $- 16$ as $- 4$ plus $- 12$

$3 y^{2} + (- 4 - 12) y + 16$

Apply the distributive property.

$3 y^{2} - 4 y - 12 y + 16$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 y^{2} - 4 y) - 12 y + 16$

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

$y (3 y - 4) - 4 (3 y - 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 4$ .

$(3 y - 4) (y - 4)$

Factor 3y^2-16y+16

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