Factor 10x^2+9x+2

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

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

Factor $9$ out of $9 x$ .

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

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

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

Apply the distributive property.

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

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$2 x (5 x + 2) + 1 (5 x + 2)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 x + 2$ .

$(5 x + 2) (2 x + 1)$

Factor 10x^2+9x+2

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