Question

if the polynomial ax^3+4x^2-3x-4andx^2-4x+a leaves the same remainder when divided by x-3 find the value of a

Answer 1

given p(x)=ax^3+4x^3-3x-4
,g(x)=x-3
let (x-3)=0
x-3=0
x=3
putting x=3
p(3)=(a(3)^3)+(4(3)^3)-(3×3)(-4)
=27a+108-9-4
=27a+108-13
=27a+95 -------(1) equation
p(x)=x^2-4x+a
g(x)=3
putting x=3
p(3)=(3)^2-4×3+a
=9-12+a
=-3+a----------(2) equation
a=????
=>ax^3+4x^2-3x-4=x^2-4x+a
=>27a+95=-3+a
=>27a-a=-3-95 (hence,sign of numbers changes because of changing position out of the equal sign)
=>26a=-98
=>a=26/98
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