Divide by using long division. \[ \left(x^{3}-3 x+6\right) \div(x-3) \] Suggested tutorial: Learn It: Divide polynomials using long division.

To perform the long division of \( x^3 - 3x + 6 \) by \( x - 3 \), you start by dividing the leading term \( x^3 \) by the leading term \( x \) of the divisor, which gives you \( x^2 \). Multiply \( x^2 \) by \( x - 3 \), resulting in \( x^3 - 3x^2 \). Subtract this from the original polynomial to get \( 3x^2 - 3x + 6 \). Next, divide \( 3x^2 \) by \( x \), giving you \( 3x \). Multiply \( 3x \) by \( x - 3 \) and subtract again. Continue this process until you've brought down all terms. Did you know that polynomial long division functions similarly to numerical long division? Instead of dividing digits, you’re dividing terms! It’s like a dance of distributing and subtracting until you have your final answer (the quotient) and maybe some leftovers (the remainder) if it doesn't divide evenly! For a deeper insight, you might want to explore synthetic division as another method for dividing polynomials. It simplifies calculations, especially when you’re dividing by linear factors like \( x - c \). It’s a faster shortcut once you get the hang of it—perfect for simplifying the process when dealing with large polynomials without losing any of that valuable polynomial knowledge along the way!