Factor 56r^2+31r+3

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

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 $31 r$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 56r^2+31r+3

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