Simplify (9z^5-8z^3+4z^2+7z)÷(-2z)

$(9 z^{5} - 8 z^{3} + 4 z^{2} + 7 z) \div (- 2 z)$

Step 1

Rewrite the division as a fraction.

$\frac{9 z^{5} - 8 z^{3} + 4 z^{2} + 7 z}{- 2 z}$

Step 2

Factor $z$ out of $9 z^{5} - 8 z^{3} + 4 z^{2} + 7 z$ .

Factor $z$ out of $9 z^{5}$ .

$\frac{z (9 z^{4}) - 8 z^{3} + 4 z^{2} + 7 z}{- 2 z}$

Factor $z$ out of $- 8 z^{3}$ .

$\frac{z (9 z^{4}) + z (- 8 z^{2}) + 4 z^{2} + 7 z}{- 2 z}$

Factor $z$ out of $4 z^{2}$ .

$\frac{z (9 z^{4}) + z (- 8 z^{2}) + z (4 z) + 7 z}{- 2 z}$

Factor $z$ out of $7 z$ .

$\frac{z (9 z^{4}) + z (- 8 z^{2}) + z (4 z) + z \cdot 7}{- 2 z}$

Factor $z$ out of $z (9 z^{4}) + z (- 8 z^{2})$ .

$\frac{z (9 z^{4} - 8 z^{2}) + z (4 z) + z \cdot 7}{- 2 z}$

Factor $z$ out of $z (9 z^{4} - 8 z^{2}) + z (4 z)$ .

$\frac{z (9 z^{4} - 8 z^{2} + 4 z) + z \cdot 7}{- 2 z}$

Factor $z$ out of $z (9 z^{4} - 8 z^{2} + 4 z) + z \cdot 7$ .

$\frac{z (9 z^{4} - 8 z^{2} + 4 z + 7)}{- 2 z}$

Step 3

Cancel the common factor of $z$ .

Cancel the common factor.

$\frac{z (9 z^{4} - 8 z^{2} + 4 z + 7)}{- 2 z}$

Rewrite the expression.

$\frac{9 z^{4} - 8 z^{2} + 4 z + 7}{- 2}$

Step 4

Move the negative in front of the fraction.

$- \frac{9 z^{4} - 8 z^{2} + 4 z + 7}{2}$