Factor 5x^2+26x+24

$5 x^{2} + 26 x + 24$

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 $b = 26$ .

Factor $26$ out of $26 x$ .

$5 x^{2} + 26 (x) + 24$

Rewrite $26$ as $6$ plus $20$

$5 x^{2} + (6 + 20) x + 24$

Apply the distributive property.

$5 x^{2} + 6 x + 20 x + 24$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 6 x) + 20 x + 24$

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

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

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 6$ .

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

Factor 5x^2+26x+24

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