Question

Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.

Answer 1

The remainder when f(x) is divided by x+3 is 76.

Step-by-step explanation:

To find the remainder when f(x) = -2x^3 + x^2 - 4x + 1 is divided by x+3, we can use the remainder theorem. According to the remainder theorem, the remainder is equal to f(-3). Substituting x = -3 into the function, we get:

f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1

= -2(-27) + 9 + 12 + 1

= 54 + 9 + 12 + 1

= 76

Therefore, the remainder when f(x) is divided by x+3 is 76.