Factor 56c^2+31c+3

$56 c^{2} + 31 c + 3$

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 $a \cdot c = 56 \cdot 3 = 168$ and whose sum is $b = 31$ .

Factor $31$ out of $31 c$ .

$56 c^{2} + 31 (c) + 3$

Rewrite $31$ as $7$ plus $24$

$56 c^{2} + (7 + 24) c + 3$

Apply the distributive property.

$56 c^{2} + 7 c + 24 c + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(56 c^{2} + 7 c) + 24 c + 3$

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

$7 c (8 c + 1) + 3 (8 c + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $8 c + 1$ .

$(8 c + 1) (7 c + 3)$

Factor 56c^2+31c+3

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