Factor 2(m+p)^2-7(m+p)-30

$2 {(m + p)}^{2} - 7 (m + p) - 30$

Step 1

Let $u = m + p$ . Substitute $u$ for all occurrences of $m + p$ .

$2 u^{2} - 7 u - 30$

Step 2

Factor by grouping.

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 $a \cdot c = 2 \cdot - 30 = - 60$ and whose sum is $b = - 7$ .

Factor $- 7$ out of $- 7 u$ .

$2 u^{2} - 7 (u) - 30$

Rewrite $- 7$ as $5$ plus $- 12$

$2 u^{2} + (5 - 12) u - 30$

Apply the distributive property.

$2 u^{2} + 5 u - 12 u - 30$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(2 u^{2} + 5 u) - 12 u - 30$

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

$u (2 u + 5) - 6 (2 u + 5)$

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

$(2 u + 5) (u - 6)$

Step 3

Replace all occurrences of $u$ with $m + p$ .

$(2 (m + p) + 5) (m + p - 6)$

Step 4

Apply the distributive property.

$(2 m + 2 p + 5) (m + p - 6)$

Factor 2(m+p)^2-7(m+p)-30

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