Question

2xcube+3xsquare+ax+b is divided by (x-2) and remains 2 and(x+2) leaves -2 find a and b

Answer 1

Given 2(xcube)+3 (xsquare)+ax+9b is divided by x -2 leaves remainder 2 and is divided by x+2 leaves remainder -2
Let f (x)=2(xcube)+3 (xsquare)+ax+b
By remainder theorem
f (2)=2×2×2×2+3×2×2+2a+b
2=16+12+2a+b
2=28+2a+b
2a+b=-26
2a=-26-b
f (-2)=2×-2×-2×-2+3×-2×-2-2a+b
-2=-16+12-2a+b
-2=-4-2a+b
2=-2a+b
b=2+2a
b=2-26-b
2b=-24
b=-12
Therefore a=(-26-b )/2
a=(-26+12)/2
a=-14/2
a=-7