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To find the remainder when the polynomial \(6x^2 + 11x - 3\) is divided by \(x + 2\), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of a polynomial \(f(x)\) when divided by \(x - a\) is equal to \(f(a)\).

In this case, the divisor is \(x + 2\), which means we set \(x = -2\). Let's evaluate the polynomial at \(x = -2\):

\[
f(x) = 6x^2 + 11x - 3
\]
\[
f(-2) = 6(-2)^2 + 11(-2) - 3
\]
\[
f(-2) = 6(4) - 22 - 3
\]
\[
f(-2) = 24 - 22 - 3
\]
\[
f(-2) = -1
\]

So, the remainder when \(6x^2 + 11x - 3\) is divided by \(x + 2\) is \(-1\).

Would you like more details or have any questions on this problem?

Here are some related questions you might find interesting:
1. How do you perform polynomial long division for \(6x^2 + 11x - 3\) divided by \(x + 2\)?
2. What is the significance of the Remainder Theorem in algebra?
3. How can synthetic division be used to divide polynomials?
4. What happens to the remainder if the divisor is a root of the polynomial?
5. How does the degree of the divisor affect the remainder in polynomial division?

**Tip:** The Remainder Theorem is a quick way to find the remainder without fully dividing the polynomial, which is especially useful for higher-degree polynomials.

What is the remainder when the polynomial 6x^2 + 11x - 3 is divided by x + 2?

Find the remainder when dividing the polynomial 6x^2 + 11x - 3 by x + 2 using the Remainder Theorem. This step-by-step solution demonstrates how to apply the theorem for polynomials and is ideal for students in Grades 9-12.

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