Factor 5x^2+31x+30

$5 x^{2} + 31 x + 30$

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 $a \cdot c = 5 \cdot 30 = 150$ and whose sum is $b = 31$ .

Factor $31$ out of $31 x$ .

$5 x^{2} + 31 (x) + 30$

Rewrite $31$ as $6$ plus $25$

$5 x^{2} + (6 + 25) x + 30$

Apply the distributive property.

$5 x^{2} + 6 x + 25 x + 30$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 6 x) + 25 x + 30$

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

$x (5 x + 6) + 5 (5 x + 6)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 6$ .

$(5 x + 6) (x + 5)$

Factor 5x^2+31x+30

Related Questions

Support LCMGCF.com by disabling your adblocker.