Question

Use remainder theorem to find the remainder when the function f(x) = x^3 + 8x^2 - 2x is divided by (x+3)

Answer 1

f(x) = x^3 + 8x^2 - 2x is divided by (x+3)

When a polynomial function f(x) divided by (x-a), then remainder is f(a)

Given that f(x) divide by (x+3)

First we set x+3 =0  and solve for x

x+3 =0  so x=-3

Now plug in -3 for x  in f(x) and find out f(-3)

f(-3) is the remainder

$f(x) = x^3 + 8x^2 - 2x$

$f(-3) = (-3)^3 + 8(-3)^2 - 2(-3)= -27 +72+6 = 51$

Remainder is 51

Answer is 51

Answer 2

Answer:

The correct option is 3.

Step-by-step explanation:

According to the remainder theorem, if a polynomial P(x) is divided by (x-c), then the remainder is equal to P(c).

The given function is

$f(x)=x^3+8x^2-2x$

Using the remainder theorem, the remainder when the function f(x) is divided by (x+3) is equal to f(-3). The remainder is

$f(-3)=(-3)^3+8(-3)^2-2(-3)$

$f(-3)=-27+8(9)+6$

$f(-3)=-27+72+6$

$f(-3)=-27+78$

$f(-3)=51$

The remainder is 51. Therefore the correct option is 3.