Factor 2x^2-9x+10

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

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 $a \cdot c = 2 \cdot 10 = 20$ and whose sum is $b = - 9$ .

Factor $- 9$ out of $- 9 x$ .

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

Rewrite $- 9$ as $- 4$ plus $- 5$

$2 x^{2} + (- 4 - 5) x + 10$

Apply the distributive property.

$2 x^{2} - 4 x - 5 x + 10$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 x^{2} - 4 x) - 5 x + 10$

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

$2 x (x - 2) - 5 (x - 2)$

Step 3

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

$(x - 2) (2 x - 5)$

Factor 2x^2-9x+10

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