Questions: Divide. 36 z^4+32 z^3+9 z^2 / 4 z^2 Simplify your answer as much as possible.

Solution Steps

To simplify the given expression, divide each term in the numerator by the term in the denominator. This involves dividing the coefficients and subtracting the exponents of like bases according to the rules of exponents.

We start with the expression

\[ \frac{36 z^{4}+32 z^{3}+9 z^{2}}{4 z^{2}}. \]

We will divide each term in the numerator by \(4 z^{2}\).

Dividing each term gives us:

\[ \frac{36 z^{4}}{4 z^{2}} + \frac{32 z^{3}}{4 z^{2}} + \frac{9 z^{2}}{4 z^{2}}. \]

Calculating each term separately:

1. \(\frac{36 z^{4}}{4 z^{2}} = 9 z^{2}\)
2. \(\frac{32 z^{3}}{4 z^{2}} = 8 z\)
3. \(\frac{9 z^{2}}{4 z^{2}} = \frac{9}{4}\)

Combining the simplified terms, we have:

\[ 9 z^{2} + 8 z + \frac{9}{4}. \]

Final Answer