Factor 10x^2+17x+6

$10 x^{2} + 17 x + 6$

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 $a \cdot c = 10 \cdot 6 = 60$ and whose sum is $b = 17$ .

Factor $17$ out of $17 x$ .

$10 x^{2} + 17 (x) + 6$

Rewrite $17$ as $5$ plus $12$

$10 x^{2} + (5 + 12) x + 6$

Apply the distributive property.

$10 x^{2} + 5 x + 12 x + 6$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 x^{2} + 5 x) + 12 x + 6$

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

$5 x (2 x + 1) + 6 (2 x + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $2 x + 1$ .

$(2 x + 1) (5 x + 6)$

Factor 10x^2+17x+6

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