Algebra 2 L. 4 Divide polynomials using long division YN5 Divide. If the polynomial does not divide evenly, include the remainder as a fraction. \( \left(28 p^{4}-149 p^{3}+55 p^{2}-56 p+30\right) \div(p-5) \) Submit

To divide \( 28p^4 - 149p^3 + 55p^2 - 56p + 30 \) by \( p - 5 \), first, set up the long division. Begin by dividing the leading term \( 28p^4 \) by \( p \), giving \( 28p^3 \). Multiply \( 28p^3 \) by \( (p - 5) \) to get \( 28p^4 - 140p^3 \). Subtract this from the original polynomial, leading to \( -9p^3 + 55p^2 - 56p + 30 \). Repeat this process for the resulting polynomial until you've reached the constant term. You'll find that the remainder is 5, giving the final result of: \[ 28p^3 - 9p^2 + 0p - 5 + \frac{5}{p - 5} \] Transforming polynomials can be tricky, but breaking down the division step-by-step makes it manageable! As a fun fact, polynomial long division resembles numerical long division. While you're working with equations instead of numbers, the principles are the same: dividing to find quotients and remainders. Understanding this connection can help make polynomial division feel less intimidating!