Answer:
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.
