Find the quotient of 18, y, to the power 5 , plus, 12, y, to the power 4 , plus, 21, y, cubed, minus, 24, y, squared18y

Question

5
+12y
4
+21y
3
−24y
2
divided by 3, y, squared3y
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

Answer 1

To simplify the expression \( \frac{18y^5 + 12y^4 + 21y^3 - 24y^2}{3y^2} \), we will break it down in a similar way to your provided example.

1. Write the Expression: \[ \frac{18y^5 + 12y^4 + 21y^3 - 24y^2}{3y^2} \]

2. Separate Each Term: We will divide each term in the numerator by \( 3y^2 \): \[ = \frac{18y^5}{3y^2} + \frac{12y^4}{3y^2} + \frac{21y^3}{3y^2} - \frac{24y^2}{3y^2} \]

3. Divide Each Term:

   • \( \frac{18y^5}{3y^2} = 6y^{5-2} = 6y^3 \)
   • \( \frac{12y^4}{3y^2} = 4y^{4-2} = 4y^2 \)
   • \( \frac{21y^3}{3y^2} = 7y^{3-2} = 7y \)
   • \( \frac{24y^2}{3y^2} = 8 \)

4. Combine the Results: Now we combine the results from each division: \[ 6y^3 + 4y^2 + 7y - 8 \]

5. Final Simplified Expression: The final result is: \[ 6y^3 + 4y^2 + 7y - 8 \]

So, the simplified expression for \( \frac{18y^5 + 12y^4 + 21y^3 - 24y^2}{3y^2} \) is \( 6y^3 + 4y^2 + 7y - 8 \).