8c^2+10c−3
Factor the expression by grouping. First, the expression needs to be rewritten as 8c^2+ac+bc−3. To find a and b, set up a system to be solved.
a+b=10
ab=8(−3)=−24
Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product −24.
−1,24
−2,12
−3,8
−4,6
Calculate the sum for each pair.
−1+24=23
−2+12=10
−3+8=5
−4+6=2
The solution is the pair that gives sum 10.
a=−2
b=12
Rewrite 8c
2
+10c−3 as (8c
2
−2c)+(12c−3).
(8c
2
−2c)+(12c−3)
Factor out 2c in the first and 3 in the second group.
2c(4c−1)+3(4c−1)
Factor out common term 4c−1 by using distributive property.
(4c−1)(2c+3)