Look at the work shown for the division problem shown on the right. the remainder is

8

Step-by-step explanation:

Given the polynomial function

f(x) = 2x⁴-4x³-11x²+3x-6 divided by x+2

We can use what is known as the remainder theorem to find the remainder.

Since x+2 is a factor of the polynomial, we will equate it to zero to get the variable x as shown

x+2 = 0

x = -2

Substituting x = -2 into the polynomial function:

f(-2) = 2(-2)⁴-4(-2)³-11(-2)²+3(-2)-6

f(-2) = 2(16)-4(-8)-11(4)-6-6

f(-2) = 32+32-44-12

f(-2) = 20-12

f(-2) = 8

Therefore, the remainder when the polynomial is divided by x+2 is 8.