Factor 12x^2+7x+1

$12 x^{2} + 7 x + 1$

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 $a \cdot c = 12 \cdot 1 = 12$ and whose sum is $b = 7$ .

Factor $7$ out of $7 x$ .

$12 x^{2} + 7 (x) + 1$

Rewrite $7$ as $3$ plus $4$

$12 x^{2} + (3 + 4) x + 1$

Apply the distributive property.

$12 x^{2} + 3 x + 4 x + 1$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 x^{2} + 3 x) + 4 x + 1$

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

$3 x (4 x + 1) + 1 (4 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 x + 1$ .

$(4 x + 1) (3 x + 1)$

Factor 12x^2+7x+1

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