Question

Find the remainder using remainder theorem, when:

$4 x^3 - 3 x^2 + 2 x - 4$ is divided by $x + 3$

Answer 1

x-a, the remainder is f(a)
x-(-3)
f(-3)=4*(-3)^3-3(-3)^2+2(-3)-4=
4*(-27)-3*9-6-4=
-108-27-6-4
-145

So the remainder is -145

Answer 2

Given polynomial

f(x) = $4 x^3 - 3 x^2 + 2 x - 4$

g(x) = x + 3

By the remainder theorem ,
If f(x) is divided by ( x - a) then it leaves a remainder f(a)

Now,
If f(x) is divided by x + 3 then it leaves a remainder f(-3)

Now,
f(-3 ) = 4(-3)³ - 3(-3)² + 2(-3)-4

= 4(-27) -3(9) -6 - 4

= -108 - 27 - 6 - 4

= -118 - 27


= -145

Therefore, If $4 x^3 - 3 x^2 + 2 x - 4$ is divided by $x + 3$ then it leaves a remainder -145