Question Show Examples If $f(x)=3 x^{5}+2 x^{3}+1$, then what is the remainder when $f(x)$ is divided by $x+2$ ? Answer Attempt 1 out of 2 Submit Answer

Step 1 ：The problem is asking for the remainder when a polynomial function, \(f(x) = 3x^5 + 2x^3 + 1\), is divided by \(x + 2\).

Step 2 ：To find this, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial \(f(x)\) divided by a linear term \((x - a)\) is equal to \(f(a)\).

Step 3 ：In this case, we need to find the remainder when \(f(x)\) is divided by \((x + 2)\), so we need to evaluate \(f(-2)\).

Step 4 ：Substituting \(-2\) into the function gives us a remainder of \(-111\).

Step 5 ：So, the remainder when \(f(x)\) is divided by \(x + 2\) is \(\boxed{-111}\).