Find the quotient of 15, x, cubed, plus, 10, x, squared, plus, 5, x, minus, 3015x

Question

3
+10x
2
+5x−30 divided by 55.

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 find the quotient of the expression \( 15x^3 + 10x^2 + 5x - 3015 \) divided by \( 55 \), we will simplify the expression similarly to the provided example.

First, we write the expression:

\[ \frac{15x^3 + 10x^2 + 5x - 3015}{55} \]

We will break this down into individual fractions:

\[ \frac{15x^3}{55} + \frac{10x^2}{55} + \frac{5x}{55} + \frac{-3015}{55} \]

Now we simplify each term separately:

1. For \( \frac{15x^3}{55} \):

   \[ \frac{15}{55}x^3 = \frac{3}{11}x^3 \]

2. For \( \frac{10x^2}{55} \):

   \[ \frac{10}{55}x^2 = \frac{2}{11}x^2 \]

3. For \( \frac{5x}{55} \):

   \[ \frac{5}{55}x = \frac{1}{11}x \]

4. For \( \frac{-3015}{55} \):

   To simplify \(-3015\) divided by \(55\), we perform the division:

   \[ -\frac{3015}{55} = -55 \] (since \( 3015 \div 55 = 55 \))

Putting it all together, we have:

\[ \frac{15x^3 + 10x^2 + 5x - 3015}{55} = \frac{3}{11}x^3 + \frac{2}{11}x^2 + \frac{1}{11}x - 55 \]

So the final answer, combining all terms is:

\[ \frac{3}{11}x^3 + \frac{2}{11}x^2 + \frac{1}{11}x - 55 \]