If \( f(x)=5 x^{6}+4 x^{5}+2 \), then what is the remainder when \( f(x) \) is divided by \( x+1 \) ? Answer Attempt 1 out of 2

To find the remainder when \( f(x) \) is divided by \( x+1 \), we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial \( f(x) \) by \( x - c \) is \( f(c) \). Here, since we want to divide by \( x + 1 \), we have \( c = -1 \). We will calculate \( f(-1) \): \[ f(-1) = 5(-1)^6 + 4(-1)^5 + 2 \] \[ = 5(1) + 4(-1) + 2 \] \[ = 5 - 4 + 2 \] \[ = 3. \] So, the remainder when \( f(x) \) is divided by \( x + 1 \) is \( \boxed{3} \).