Factor 18x^2-27x-5

$18 x^{2} - 27 x - 5$

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 $a \cdot c = 18 \cdot - 5 = - 90$ and whose sum is $b = - 27$ .

Factor $- 27$ out of $- 27 x$ .

$18 x^{2} - 27 (x) - 5$

Rewrite $- 27$ as $3$ plus $- 30$

$18 x^{2} + (3 - 30) x - 5$

Apply the distributive property.

$18 x^{2} + 3 x - 30 x - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(18 x^{2} + 3 x) - 30 x - 5$

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

$3 x (6 x + 1) - 5 (6 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $6 x + 1$ .

$(6 x + 1) (3 x - 5)$

Factor 18x^2-27x-5

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