To find the answer using the remainder theorem, you need to divide (4x³ + 2x² + 3x + 1) by (x+2). The remainder of that will be the value of the function at x=-2, which as you've already found, is -29.

]]>4(-2)^3 + 2(-2)^2 + 3(-2) + 1

-32 + 8 + (-6) + 1

-32 + 8 - 6 + 1

-24 - 6 + 1

-30 + 1

-29