Factor 6y^2-17y+5

$6 y^{2} - 17 y + 5$

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 $a \cdot c = 6 \cdot 5 = 30$ and whose sum is $b = - 17$ .

Factor $- 17$ out of $- 17 y$ .

$6 y^{2} - 17 (y) + 5$

Rewrite $- 17$ as $- 2$ plus $- 15$

$6 y^{2} + (- 2 - 15) y + 5$

Apply the distributive property.

$6 y^{2} - 2 y - 15 y + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 y^{2} - 2 y) - 15 y + 5$

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

$2 y (3 y - 1) - 5 (3 y - 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 y - 1$ .

$(3 y - 1) (2 y - 5)$

Factor 6y^2-17y+5

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