Factor 3c^2+14c+8

$3 c^{2} + 14 c + 8$

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 $a \cdot c = 3 \cdot 8 = 24$ and whose sum is $b = 14$ .

Factor $14$ out of $14 c$ .

$3 c^{2} + 14 (c) + 8$

Rewrite $14$ as $2$ plus $12$

$3 c^{2} + (2 + 12) c + 8$

Apply the distributive property.

$3 c^{2} + 2 c + 12 c + 8$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 c^{2} + 2 c) + 12 c + 8$

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

$c (3 c + 2) + 4 (3 c + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 c + 2$ .

$(3 c + 2) (c + 4)$

Factor 3c^2+14c+8

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