Factor 8x^2+59x+21

$8 x^{2} + 59 x + 21$

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 $a \cdot c = 8 \cdot 21 = 168$ and whose sum is $b = 59$ .

Factor $59$ out of $59 x$ .

$8 x^{2} + 59 (x) + 21$

Rewrite $59$ as $3$ plus $56$

$8 x^{2} + (3 + 56) x + 21$

Apply the distributive property.

$8 x^{2} + 3 x + 56 x + 21$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(8 x^{2} + 3 x) + 56 x + 21$

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

$x (8 x + 3) + 7 (8 x + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $8 x + 3$ .

$(8 x + 3) (x + 7)$

Factor 8x^2+59x+21

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