Factor 7x^2+24x+9

$7 x^{2} + 24 x + 9$

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 $a \cdot c = 7 \cdot 9 = 63$ and whose sum is $b = 24$ .

Factor $24$ out of $24 x$ .

$7 x^{2} + 24 (x) + 9$

Rewrite $24$ as $3$ plus $21$

$7 x^{2} + (3 + 21) x + 9$

Apply the distributive property.

$7 x^{2} + 3 x + 21 x + 9$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(7 x^{2} + 3 x) + 21 x + 9$

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

$x (7 x + 3) + 3 (7 x + 3)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $7 x + 3$ .

$(7 x + 3) (x + 3)$

Factor 7x^2+24x+9

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