Factor 5x^2+23x+12

$5 x^{2} + 23 x + 12$

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 $a \cdot c = 5 \cdot 12 = 60$ and whose sum is $b = 23$ .

Factor $23$ out of $23 x$ .

$5 x^{2} + 23 (x) + 12$

Rewrite $23$ as $3$ plus $20$

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

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

Step 3

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

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

Factor 5x^2+23x+12

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