Questions: Polynomials and Factoring Dividing a polynomial by a monomial: Try Again Your answer is incorrect. Divide. (-23 u^5 z^7+20 u^5 z) div(-4 u^2 z^4) Simplify your answer as much as possible

Solution Steps

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial separately. Simplify each resulting term by reducing the coefficients and subtracting the exponents of like bases.

We start with the polynomial \( -23 u^{5} z^{7} + 20 u^{5} z \) and the monomial \( -4 u^{2} z^{4} \).

We divide each term of the polynomial by the monomial: \[ \frac{-23 u^{5} z^{7}}{-4 u^{2} z^{4}} + \frac{20 u^{5} z}{-4 u^{2} z^{4}} \]

1. For the first term: \[ \frac{-23 u^{5} z^{7}}{-4 u^{2} z^{4}} = \frac{23}{4} u^{5-2} z^{7-4} = \frac{23}{4} u^{3} z^{3} \]

2. For the second term: \[ \frac{20 u^{5} z}{-4 u^{2} z^{4}} = \frac{-20}{4} u^{5-2} z^{1-4} = -5 u^{3} z^{-3} \]

Combining the simplified terms, we have: \[ \frac{23}{4} u^{3} z^{3} - 5 u^{3} z^{-3} \]

Factoring out \( u^{3} \) gives: \[ u^{3} \left( \frac{23}{4} z^{3} - 5 z^{-3} \right) \]

Final Answer