Answer to Question #10702 in Algebra for Manthan khorwal

Question

The polynomials ax3-3x2+4 and 2x3-5x+a a when divided by (x-2) leave the remainders p and q respectively.If p-2q+4, find the value of a.

Answer 1

If p,q are remainders when we are dividing by (x-2) then

f(x)=ax^3-3x^2+4
g(x)=2x^3-5x+a

f(2)=p
g(2)=q

8a-12+4=p
16-10+a=q

p=8a-8
q=a+6

If
p-2q=4 then 8a-8-2(a+6)=4 and so 6a=24 => a=4 - answer