Factor 2a^2-9a-45

$2 a^{2} - 9 a - 45$

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 $a \cdot c = 2 \cdot - 45 = - 90$ and whose sum is $b = - 9$ .

Factor $- 9$ out of $- 9 a$ .

$2 a^{2} - 9 (a) - 45$

Rewrite $- 9$ as $6$ plus $- 15$

$2 a^{2} + (6 - 15) a - 45$

Apply the distributive property.

$2 a^{2} + 6 a - 15 a - 45$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 a^{2} + 6 a) - 15 a - 45$

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

$2 a (a + 3) - 15 (a + 3)$

Step 3

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

$(a + 3) (2 a - 15)$

Factor 2a^2-9a-45

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