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.

$3 x (4 x - 1) - (4 x - 1)$

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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