\( \frac{x^{5}+x^{3}-5}{x-2} \) \( \begin{array}{ll}\text { A. } x^{4}+2 x^{3}+5 x^{2}+10 x+20+\frac{35}{x-2} & \text { C. } x^{4}-x^{3}-\frac{3}{x-2} \\ \text { B. } x^{4}-2 x^{3}+5 x^{2}-10 x+20-\frac{45}{x-2} & \text { D. } x^{4}+3 x^{3}+\frac{1}{x-2}\end{array} \)
Real Tutor Solution
Answer
Solution
Reviewed and approved by the UpStudy tutoring team
Explain 
Simplify this solution Beyond the Answer
To divide the polynomial \( x^{5}+x^{3}-5 \) by \( x-2 \), we can use polynomial long division. First, divide the leading term \( x^5 \) by \( x \), which gives \( x^4 \). Then, multiply \( x^4 \) by \( x-2 \) and subtract it from the original polynomial. Continue this process until the remainder is a degree lower than the divisor. Eventually, you'll arrive at a quotient plus a remainder. This division process can sometimes seem a bit perplexing, but it's a powerful tool in algebra that lets us break down complex polynomials into simpler forms! Feeling overwhelmed? You're not alone! A common mistake during polynomial long division is forgetting to subtract correctly. Make sure to carefully write down each subtraction step, as it's easy to lose track and mix up the signs! It also helps to check your work by multiplying the quotient by the divisor and adding the remainder, ensuring you get back to the original polynomial. Happy dividing!
