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Px²-x+Q is divisible by 3x+2, so
3x+2=0
x=-2/3
When x=-2/3,
P(-2/3)²-(-2/3)+Q=0
⁴/9P+⅔+Q=0
Multiply through by the L.C.M
(4P+6+9Q)/9=0
4P+9Q=-6 ....equ i
Also, when Px²-x+Q is divided by x-1 the remainder is -5,
Therefore, x-1=0
x=1
P(1)²-1+Q=-5
P+Q=-5+1
P+Q=-4 .....equ ii
From equ ii,
Q=-4-P ....equ iii
4P+9Q=-6
4P+9(-4-P)=-6
4P-36-9P=-6
-5P=-6+36
-5P=30
P=30/-5=-6
Sub the value of P into equ. iii
Q=-4-P
Q=-4-(-6)
Q=-4+6
Q=2
P,Q=(-6,2)