Answer:
Solution Steps
m
2
−13m−30
Factor the expression by grouping. First, the expression needs to be rewritten as m
2
+am+bm−30. To find a and b, set up a system to be solved.
a+b=−13
ab=1(−30)=−30
Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product −30.
1,−30
2,−15
3,−10
5,−6
Calculate the sum for each pair.
1−30=−29
2−15=−13
3−10=−7
5−6=−1
The solution is the pair that gives sum −13.
a=−15
b=2
Rewrite m
2
−13m−30 as (m
2
−15m)+(2m−30).
(m
2
−15m)+(2m−30)
Factor out m in the first and 2 in the second group.
m(m−15)+2(m−15)
Factor out common term m−15 by using distributive property.
(m−15)(m+2)