Let p(x)=x4−2x3+3x2−ax+b
p(−1)=19;p(1)=5 [1 Mark]
p(−1)=(−1)4−2(−1)3+3(−1)2−a(−1)+b=19
a+b=13...............(1)
p(1)=(1)4−2(1)3+3(1)2−a(1)+b=5
−a+b=3................(2)
On solving (1) and (2), we get a=5,b=8 [1 Mark]
p(x)=x4−2x3+3x2−5x+8
When p(x) is divided by(x-3),
Remainder = p(3)=(3)4−2(3)3+3(3)2−5(3)+8 [1 Mark]
p(3)=47