Factor 3p^2-2p-5

$3 p^{2} - 2 p - 5$

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 $b = - 2$ .

Factor $- 2$ out of $- 2 p$ .

$3 p^{2} - 2 (p) - 5$

Rewrite $- 2$ as $3$ plus $- 5$

$3 p^{2} + (3 - 5) p - 5$

Apply the distributive property.

$3 p^{2} + 3 p - 5 p - 5$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(3 p^{2} + 3 p) - 5 p - 5$

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

$3 p (p + 1) - 5 (p + 1)$

Step 3

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

$(p + 1) (3 p - 5)$

Factor 3p^2-2p-5

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