1. POTW #5
Solution
By : Matthew Tetreault
For the week of 3/12/12 to 3/15/12

2. If (x+2) and (x-3) are factors of the polynomial
P(x)=x5-5x4-x3+19x2+ax+b
then find a+b
P(-2)=(-2)5-5(-2)4-(-2)3+19(-2)2+a(-2)+b=0
P(-2)=-32-80+8+76-2a+b=0
P(-2)=-28-2a+b=0
P(3)=(3)5-5(3)4-(3)3+19(3)2+a(3)+b=0
P(3)=243-405-27+171+3a+b=0
P(3)=-18+3a+b=0
set equal to each other
-18+3a+b=-28-2a+b
5a=-10
a=-2
-18+3(-2)+b=0
-24+b=0
b=24
A+B
-2+24=22