Factor 12b^2+43b+35

$12 b^{2} + 43 b + 35$

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 $a \cdot c = 12 \cdot 35 = 420$ and whose sum is $b = 43$ .

Factor $43$ out of $43 b$ .

$12 b^{2} + 43 (b) + 35$

Rewrite $43$ as $15$ plus $28$

$12 b^{2} + (15 + 28) b + 35$

Apply the distributive property.

$12 b^{2} + 15 b + 28 b + 35$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 b^{2} + 15 b) + 28 b + 35$

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

$3 b (4 b + 5) + 7 (4 b + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $4 b + 5$ .

$(4 b + 5) (3 b + 7)$

Factor 12b^2+43b+35

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