Answer:
The remainder is -61
Step-by-step explanation:
The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-r) is equal to f(r).
The given polynomial is:
[tex]f(x) = 4x^3 - 6x^2 + 3x + 1[/tex]
We need to find the remainder when f(x) is divided by x+2. According to the above-mentioned theorem, we only need to find f(-2) as follows:
[tex]f(-2) = 4(-2)^3 - 6(-2)^2 + 3(-2) + 1[/tex]
[tex]f(-2) = 4(-8) - 6(4) - 6 + 1[/tex]
[tex]f(-2) = -32 - 24 - 6 + 1=-61[/tex]
The remainder is -61
