Answer: (p−8)(p−4)
Step-by-step explanation: p
2
−12p+32
Factor the expression by grouping. First, the expression needs to be rewritten as p
2
+ap+bp+32. To find a and b, set up a system to be solved.
a+b=−12
ab=1×32=32
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 32.
−1,−32
−2,−16
−4,−8
Calculate the sum for each pair.
−1−32=−33
−2−16=−18
−4−8=−12
The solution is the pair that gives sum −12.
a=−8
b=−4
Rewrite p
2
−12p+32 as (p
2
−8p)+(−4p+32).
(p
2
−8p)+(−4p+32)
Factor out p in the first and −4 in the second group.
p(p−8)−4(p−8)
Factor out common term p−8 by using distributive property.
(p−8)(p−4)