solve using mid term splitting
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p
2
+6p−16
Factor the expression by grouping. First, the expression needs to be rewritten as p
2
+ap+bp−16. To find a and b, set up a system to be solved.
a+b=6
ab=1(−16)=−16
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 −16.
−1,16
−2,8
−4,4
Calculate the sum for each pair.
−1+16=15
−2+8=6
−4+4=0
The solution is the pair that gives sum 6.
a=−2
b=8
Rewrite p
2
+6p−16 as (p
2
−2p)+(8p−16).
(p
2
−2p)+(8p−16)
Factor out p in the first and 8 in the second group.
p(p−2)+8(p−2)
Factor out common term p−2 by using distributive property.
(p−2)(p+8)
Step-by-step explanation:
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