Factor 42x^2-35x+7

$42 x^{2} - 35 x + 7$

Step 1

Factor $7$ out of $42 x^{2} - 35 x + 7$ .

Factor $7$ out of $42 x^{2}$ .

$7 (6 x^{2}) - 35 x + 7$

Factor $7$ out of $- 35 x$ .

$7 (6 x^{2}) + 7 (- 5 x) + 7$

Factor $7$ out of $7$ .

$7 (6 x^{2}) + 7 (- 5 x) + 7 (1)$

Factor $7$ out of $7 (6 x^{2}) + 7 (- 5 x)$ .

$7 (6 x^{2} - 5 x) + 7 (1)$

Factor $7$ out of $7 (6 x^{2} - 5 x) + 7 (1)$ .

$7 (6 x^{2} - 5 x + 1)$

Step 2

Factor.

Factor by grouping.

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 $a \cdot c = 6 \cdot 1 = 6$ and whose sum is $b = - 5$ .

Factor $- 5$ out of $- 5 x$ .

$7 (6 x^{2} - 5 (x) + 1)$

Rewrite $- 5$ as $- 2$ plus $- 3$

$7 (6 x^{2} + (- 2 - 3) x + 1)$

Apply the distributive property.

$7 (6 x^{2} - 2 x - 3 x + 1)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$7 ((6 x^{2} - 2 x) - 3 x + 1)$

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

$7 (2 x (3 x - 1) - (3 x - 1))$

Factor the polynomial by factoring out the greatest common factor, $3 x - 1$ .

$7 ((3 x - 1) (2 x - 1))$

Remove unnecessary parentheses.

$7 (3 x - 1) (2 x - 1)$

Factor 42x^2-35x+7

Related Questions

Support LCMGCF.com by disabling your adblocker.