Factor 6b^2-13b+6

$6 b^{2} - 13 b + 6$

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 $a \cdot c = 6 \cdot 6 = 36$ and whose sum is $b = - 13$ .

Factor $- 13$ out of $- 13 b$ .

$6 b^{2} - 13 (b) + 6$

Rewrite $- 13$ as $- 4$ plus $- 9$

$6 b^{2} + (- 4 - 9) b + 6$

Apply the distributive property.

$6 b^{2} - 4 b - 9 b + 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 b^{2} - 4 b) - 9 b + 6$

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

$2 b (3 b - 2) - 3 (3 b - 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 b - 2$ .

$(3 b - 2) (2 b - 3)$

Factor 6b^2-13b+6

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