Factor 2x^2+x-45

$2 x^{2} + x - 45$

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 $b = 1$ .

Multiply by $1$ .

$2 x^{2} + 1 x - 45$

Rewrite $1$ as $- 9$ plus $10$

$2 x^{2} + (- 9 + 10) x - 45$

Apply the distributive property.

$2 x^{2} - 9 x + 10 x - 45$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 9 x) + 10 x - 45$

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

$x (2 x - 9) + 5 (2 x - 9)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x - 9$ .

$(2 x - 9) (x + 5)$

Factor 2x^2+x-45

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