Factor 3w^2+8w+5

$3 w^{2} + 8 w + 5$

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 $a \cdot c = 3 \cdot 5 = 15$ and whose sum is $b = 8$ .

Factor $8$ out of $8 w$ .

$3 w^{2} + 8 (w) + 5$

Rewrite $8$ as $3$ plus $5$

$3 w^{2} + (3 + 5) w + 5$

Apply the distributive property.

$3 w^{2} + 3 w + 5 w + 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 w^{2} + 3 w) + 5 w + 5$

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

$3 w (w + 1) + 5 (w + 1)$

Step 3

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

$(w + 1) (3 w + 5)$

Factor 3w^2+8w+5

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