Factor 5x^2+34x+24

$5 x^{2} + 34 x + 24$

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 $a \cdot c = 5 \cdot 24 = 120$ and whose sum is $b = 34$ .

Factor $34$ out of $34 x$ .

$5 x^{2} + 34 (x) + 24$

Rewrite $34$ as $4$ plus $30$

$5 x^{2} + (4 + 30) x + 24$

Apply the distributive property.

$5 x^{2} + 4 x + 30 x + 24$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 4 x) + 30 x + 24$

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

$x (5 x + 4) + 6 (5 x + 4)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 4$ .

$(5 x + 4) (x + 6)$

Factor 5x^2+34x+24

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