Factor 3x^2+17x+20

$3 x^{2} + 17 x + 20$

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 $a \cdot c = 3 \cdot 20 = 60$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$3 x^{2} + 17 (x) + 20$

Rewrite $17$ as $5$ plus $12$

$3 x^{2} + (5 + 12) x + 20$

Apply the distributive property.

$3 x^{2} + 5 x + 12 x + 20$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 x^{2} + 5 x) + 12 x + 20$

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

$x (3 x + 5) + 4 (3 x + 5)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $3 x + 5$ .

$(3 x + 5) (x + 4)$

Factor 3x^2+17x+20

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