Question

If the polynomial ax³+4x²+3x-4 and x³-4x +a leaves the same remainder when divided by x-3 then find the value of a

Answer 1

According to remainder theorem, if f(x) is divided by (x-a)then remainder
is f(a)
f(x) = ax³+4x²+3x-4
g(x)= x³-4x +a

f(3)=A(27)+4(9)+3(3)-4
27a+41
g(3)=27-4(3)+a
15+a
f(3)=G(3)
27a+41=15+a
26a=15-41
a=15-41/26
a=-26/26
a=-1

Answer 2

let f (x)=ax^3+4x^2+3x-4
and let g (x)=x^3-4x+a
zero of the poynomial of x-3 is 3
according to problem,
f (3)=g (3)
a (3)^3+4 (3)^2+3 (3)-4=27-4 (3)+a
27a+36+9-4=27-12+a
27a+41=15+a
27a-a=15-41
26a= -26
a= -26/26
a= -1