Divide the following expression: \( \frac{4 x^{8}+8 x^{6}-12 x^{2}}{4 x^{2}} \) a.) \( x^{4}+2 x^{3}-3 \) b.) \( x^{6}+2 x^{4}-3 \) c.) \( x^{6}+2 x^{4}-3 x^{2} \) d.) \( x^{4}+2 x^{3}-3 x^{2} \)

First, let's simplify the expression \( \frac{4 x^{8}+8 x^{6}-12 x^{2}}{4 x^{2}} \) by dividing each term in the numerator by \( 4 x^{2} \): 1. \( \frac{4 x^{8}}{4 x^{2}} = x^{6} \) 2. \( \frac{8 x^{6}}{4 x^{2}} = 2 x^{4} \) 3. \( \frac{-12 x^{2}}{4 x^{2}} = -3 \) Putting it all together, we have: \( x^{6} + 2 x^{4} - 3 \) So the correct answer is: **b.) \( x^{6}+2 x^{4}-3 \)** --- Did you know that polynomial long division isn't just a math trick for classrooms? It’s also a technique frequently used in computer algebra systems to manipulate algebraic expressions and simplify computations! Who knew math could have real-world tech applications? If you’re looking to sharpen your polynomial division skills, check out some online math platforms that offer practice problems and interactive lessons. Playing educational games related to algebra is an entertaining way to build your skills while having fun!