Factor 3x^2+20x+32

$3 x^{2} + 20 x + 32$

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 $a \cdot c = 3 \cdot 32 = 96$ and whose sum is $b = 20$ .

Factor $20$ out of $20 x$ .

$3 x^{2} + 20 (x) + 32$

Rewrite $20$ as $8$ plus $12$

$3 x^{2} + (8 + 12) x + 32$

Apply the distributive property.

$3 x^{2} + 8 x + 12 x + 32$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + 8 x) + 12 x + 32$

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

$x (3 x + 8) + 4 (3 x + 8)$

Step 3

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

$(3 x + 8) (x + 4)$

Factor 3x^2+20x+32

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