Factor 6x^2+37x+6

$6 x^{2} + 37 x + 6$

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 $b = 37$ .

Factor $37$ out of $37 x$ .

$6 x^{2} + 37 (x) + 6$

Rewrite $37$ as $1$ plus $36$

$6 x^{2} + (1 + 36) x + 6$

Apply the distributive property.

$6 x^{2} + 1 x + 36 x + 6$

Multiply $x$ by $1$ .

$6 x^{2} + x + 36 x + 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(6 x^{2} + x) + 36 x + 6$

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

$x (6 x + 1) + 6 (6 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x + 1$ .

$(6 x + 1) (x + 6)$

Factor 6x^2+37x+6

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