Factor 7x^2-31x+12

$7 x^{2} - 31 x + 12$

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 $a \cdot c = 7 \cdot 12 = 84$ and whose sum is $b = - 31$ .

Factor $- 31$ out of $- 31 x$ .

$7 x^{2} - 31 (x) + 12$

Rewrite $- 31$ as $- 3$ plus $- 28$

$7 x^{2} + (- 3 - 28) x + 12$

Apply the distributive property.

$7 x^{2} - 3 x - 28 x + 12$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} - 3 x) - 28 x + 12$

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

$x (7 x - 3) - 4 (7 x - 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x - 3$ .

$(7 x - 3) (x - 4)$

Factor 7x^2-31x+12

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