\( \begin{array}{ll}\text { 9) } \frac{12 x^{2}-7 x-6}{3 x-4} & \text { 10) } \frac{x^{3}+10 x^{2}+12 x+27}{x^{2}+x+3} \\ \text { 11) } \frac{5 x^{4}-2 x-3 x^{3}+2}{x^{2}-x-1} & \text { 12) } \frac{7 x^{3} y^{2}-7 x y^{3}-14 x+27}{x+2 y-1}\end{array} \)
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Let's dive into some fun insights on polynomial long division, the process you might be using here! When you perform polynomial long division, the goal is to divide a polynomial by a smaller degree polynomial, similar to how you'd do with numbers. It's like playing a game of "divide and conquer." Just remember to align your terms by degree and don’t forget to bring down the next term as necessary. Each step gives you either a term in your quotient or a remainder—just like how getting to the end of each puzzle piece creates the bigger picture of the polynomial! Once you grasp this method, you'll find that polynomial long division can be applied in various real-world scenarios, from calculating trajectories in physics to optimizing functions in economics! It helps to simplify complex expressions, making it easier to analyze systems or model behaviors. Who knew math could be so widely useful? Whether you’re calculating parceling out dough in a bakery or computing areas in physics, the skills you hone here will come in handy!
