Factor 7x^2+55x+42

$7 x^{2} + 55 x + 42$

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 $a \cdot c = 7 \cdot 42 = 294$ and whose sum is $b = 55$ .

Factor $55$ out of $55 x$ .

$7 x^{2} + 55 (x) + 42$

Rewrite $55$ as $6$ plus $49$

$7 x^{2} + (6 + 49) x + 42$

Apply the distributive property.

$7 x^{2} + 6 x + 49 x + 42$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + 6 x) + 49 x + 42$

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

$x (7 x + 6) + 7 (7 x + 6)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 6$ .

$(7 x + 6) (x + 7)$

Factor 7x^2+55x+42

Related Questions

Support LCMGCF.com by disabling your adblocker.