Find the quotient of minus, 20, y, cubed, minus, 40, y, squared−20y
3
−40y
2
divided by minus, 5, y, squared−5y
2
.
Solve the problem just like the example below
⬇️
Simplify:
start fraction, minus, 18, z, to the power 5 , plus, 3, z, to the power 4 , plus, 18, z, cubed, plus, 9, z, squared, divided by, minus, 3, z, squared, end fraction
−3z
2
−18z
5
+3z
4
+18z
3
+9z
2
minus, start fraction, 18, z, to the power 5 , divided by, minus, 3, z, squared, end fraction, plus, start fraction, 3, z, to the power 4 , divided by, minus, 3, z, squared, end fraction, plus, start fraction, 18, z, cubed, divided by, minus, 3, z, squared, end fraction, plus, start fraction, 9, z, squared, divided by, minus, 3, z, squared, end fraction
−
−3z
2
18z
5
+
−3z
2
3z
4
+
−3z
2
18z
3
+
−3z
2
9z
2
minus, left parenthesis, minus, 6, z, cubed, right parenthesis, plus, left parenthesis, minus, z, squared, right parenthesis, plus, left parenthesis, minus, 6, z, right parenthesis, plus, left parenthesis, minus, 3, right parenthesis
−(−6z
3
)+(−z
2
)+(−6z)+(−3)
6, z, cubed, minus, z, squared, minus, 6, z, minus, 3
6z
3
−z
2
−6z−3
1 answer
To find the quotient of \(-20y^3 - 40y^2 - 20y\) divided by \(-5y^2\), we can simplify as follows:
We start with the expression:
\[
\frac{-20y^3 - 40y^2 - 20y}{-5y^2}
\]
We can split the expression into separate fractions:
\[
\frac{-20y^3}{-5y^2} + \frac{-40y^2}{-5y^2} + \frac{-20y}{-5y^2}
\]
Now, we simplify each term individually:
- For the first term:
\[
\frac{-20y^3}{-5y^2} = \frac{20y^3}{5y^2} = 4y^{3-2} = 4y
\]
- For the second term:
\[
\frac{-40y^2}{-5y^2} = \frac{40y^2}{5y^2} = 8
\]
- For the third term:
\[
\frac{-20y}{-5y^2} = \frac{20y}{5y^2} = 4y^{-1} = \frac{4}{y}
\]
Now we combine the simplified terms:
\[
4y + 8 + \frac{4}{y}
\]
Thus, the final simplified expression for the quotient is:
\[
4y + 8 + \frac{4}{y}
\]
