Factor 5x^2+39x+54

$5 x^{2} + 39 x + 54$

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 $a \cdot c = 5 \cdot 54 = 270$ and whose sum is $b = 39$ .

Factor $39$ out of $39 x$ .

$5 x^{2} + 39 (x) + 54$

Rewrite $39$ as $9$ plus $30$

$5 x^{2} + (9 + 30) x + 54$

Apply the distributive property.

$5 x^{2} + 9 x + 30 x + 54$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(5 x^{2} + 9 x) + 30 x + 54$

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

$x (5 x + 9) + 6 (5 x + 9)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 9$ .

$(5 x + 9) (x + 6)$

Factor 5x^2+39x+54

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