Factor 35x^2+62x+24

$35 x^{2} + 62 x + 24$

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 $a \cdot c = 35 \cdot 24 = 840$ and whose sum is $b = 62$ .

Factor $62$ out of $62 x$ .

$35 x^{2} + 62 (x) + 24$

Rewrite $62$ as $20$ plus $42$

$35 x^{2} + (20 + 42) x + 24$

Apply the distributive property.

$35 x^{2} + 20 x + 42 x + 24$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(35 x^{2} + 20 x) + 42 x + 24$

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

$5 x (7 x + 4) + 6 (7 x + 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 4$ .

$(7 x + 4) (5 x + 6)$

Factor 35x^2+62x+24

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