Factor 10b^2+17b+3

$10 b^{2} + 17 b + 3$

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 $a \cdot c = 10 \cdot 3 = 30$ and whose sum is $b = 17$ .

Factor $17$ out of $17 b$ .

$10 b^{2} + 17 (b) + 3$

Rewrite $17$ as $2$ plus $15$

$10 b^{2} + (2 + 15) b + 3$

Apply the distributive property.

$10 b^{2} + 2 b + 15 b + 3$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(10 b^{2} + 2 b) + 15 b + 3$

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

$2 b (5 b + 1) + 3 (5 b + 1)$

Step 3

Factor the polynomial by factoring out the greatest common factor, $5 b + 1$ .

$(5 b + 1) (2 b + 3)$

Factor 10b^2+17b+3

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