Question
Use the long division method to find the result when 8, x, cubed, plus, 30, x, squared, plus, 30, x, plus, 98x
3
+30x
2
+30x+9 is divided by 4, x, plus, 34x+3.
Solve the problem just like the example below
⬇️
Use the long division method to find the result when
4, x, cubed, plus, 5, x, squared, plus, 5, x, plus, 1
4x
3
+5x
2
+5x+1 is divided by
4, x, plus, 1
4x+1.
Use Long Division:
Use Long Division:
x, squared
x
2
plus, x
+x
plus, 1
+1
4, x
4x
plus, 1
+1
right parenthesis
)
4, x, cubed
4x
3
plus, 5, x, squared
+5x
2
plus, 5, x
+5x
plus, 1
+1
start superscript, minus, end superscript, 4, x, cubed
−
4x
3
plus, start superscript, minus, end superscript, x, squared
+
−
x
2
4, x, squared
4x
2
plus, 5, x
+5x
plus, 1
+1
start superscript, minus, end superscript, 4, x, squared
−
4x
2
plus, start superscript, minus, end superscript, x
+
−
x
4, x
4x
plus, 1
+1
start superscript, minus, end superscript, 4, x
−
4x
plus, start superscript, minus, end superscript, 1
+
−
1
0
0
Answer: , x, squared, plus, x, plus, 1
Answer: x
2
+x+1
3
+30x
2
+30x+9 is divided by 4, x, plus, 34x+3.
Solve the problem just like the example below
⬇️
Use the long division method to find the result when
4, x, cubed, plus, 5, x, squared, plus, 5, x, plus, 1
4x
3
+5x
2
+5x+1 is divided by
4, x, plus, 1
4x+1.
Use Long Division:
Use Long Division:
x, squared
x
2
plus, x
+x
plus, 1
+1
4, x
4x
plus, 1
+1
right parenthesis
)
4, x, cubed
4x
3
plus, 5, x, squared
+5x
2
plus, 5, x
+5x
plus, 1
+1
start superscript, minus, end superscript, 4, x, cubed
−
4x
3
plus, start superscript, minus, end superscript, x, squared
+
−
x
2
4, x, squared
4x
2
plus, 5, x
+5x
plus, 1
+1
start superscript, minus, end superscript, 4, x, squared
−
4x
2
plus, start superscript, minus, end superscript, x
+
−
x
4, x
4x
plus, 1
+1
start superscript, minus, end superscript, 4, x
−
4x
plus, start superscript, minus, end superscript, 1
+
−
1
0
0
Answer: , x, squared, plus, x, plus, 1
Answer: x
2
+x+1
Answers
GPT-4o mini
To divide \( 8x^3 + 30x^2 + 30x + 9 \) by \( 4x + 3 \) using long division, follow these steps:
**Step 1: Set up the long division**
```
___________________________
4x + 3 | 8x^3 + 30x^2 + 30x + 9
```
**Step 2: Divide the leading term**
Divide the leading term of the dividend (\(8x^3\)) by the leading term of the divisor (\(4x\)):
\[
\frac{8x^3}{4x} = 2x^2
\]
**Step 3: Multiply and subtract**
Now, multiply \(2x^2\) by the entire divisor \(4x + 3\) and subtract from the original polynomial:
\[
2x^2(4x + 3) = 8x^3 + 6x^2
\]
Subtract this from the original polynomial:
\[
\begin{array}{r}
8x^3 + 30x^2 + 30x + 9 \\
- (8x^3 + 6x^2) \\
\hline
0 + 24x^2 + 30x + 9 \\
\end{array}
\]
**Step 4: Repeat the process**
Now, bring down the next term(s) and repeat. We will now divide \(24x^2\) by \(4x\):
\[
\frac{24x^2}{4x} = 6x
\]
Multiply \(6x\) by \(4x + 3\):
\[
6x(4x + 3) = 24x^2 + 18x
\]
Subtract this from the current polynomial:
\[
\begin{array}{r}
24x^2 + 30x + 9 \\
- (24x^2 + 18x) \\
\hline
0 + 12x + 9 \\
\end{array}
\]
**Step 5: Repeat again**
Now, divide \(12x\) by \(4x\):
\[
\frac{12x}{4x} = 3
\]
Multiply \(3\) by \(4x + 3\):
\[
3(4x + 3) = 12x + 9
\]
Subtract this from the current polynomial:
\[
\begin{array}{r}
12x + 9 \\
- (12x + 9) \\
\hline
0 \\
\end{array}
\]
**Final Result**
Since there is no remainder, we completed the division.
The answer to \( \frac{8x^3 + 30x^2 + 30x + 9}{4x + 3} \) is:
\[
\text{Answer: } 2x^2 + 6x + 3
\]
**Step 1: Set up the long division**
```
___________________________
4x + 3 | 8x^3 + 30x^2 + 30x + 9
```
**Step 2: Divide the leading term**
Divide the leading term of the dividend (\(8x^3\)) by the leading term of the divisor (\(4x\)):
\[
\frac{8x^3}{4x} = 2x^2
\]
**Step 3: Multiply and subtract**
Now, multiply \(2x^2\) by the entire divisor \(4x + 3\) and subtract from the original polynomial:
\[
2x^2(4x + 3) = 8x^3 + 6x^2
\]
Subtract this from the original polynomial:
\[
\begin{array}{r}
8x^3 + 30x^2 + 30x + 9 \\
- (8x^3 + 6x^2) \\
\hline
0 + 24x^2 + 30x + 9 \\
\end{array}
\]
**Step 4: Repeat the process**
Now, bring down the next term(s) and repeat. We will now divide \(24x^2\) by \(4x\):
\[
\frac{24x^2}{4x} = 6x
\]
Multiply \(6x\) by \(4x + 3\):
\[
6x(4x + 3) = 24x^2 + 18x
\]
Subtract this from the current polynomial:
\[
\begin{array}{r}
24x^2 + 30x + 9 \\
- (24x^2 + 18x) \\
\hline
0 + 12x + 9 \\
\end{array}
\]
**Step 5: Repeat again**
Now, divide \(12x\) by \(4x\):
\[
\frac{12x}{4x} = 3
\]
Multiply \(3\) by \(4x + 3\):
\[
3(4x + 3) = 12x + 9
\]
Subtract this from the current polynomial:
\[
\begin{array}{r}
12x + 9 \\
- (12x + 9) \\
\hline
0 \\
\end{array}
\]
**Final Result**
Since there is no remainder, we completed the division.
The answer to \( \frac{8x^3 + 30x^2 + 30x + 9}{4x + 3} \) is:
\[
\text{Answer: } 2x^2 + 6x + 3
\]