Answer :
To solve the problem of finding the quotient of the polynomial 1x + 5 when divided by (x - 2) using synthetic division, let's go through the process step-by-step:
1. Set up the Synthetic Division:
- Identify the divisor (x - 2) and note its root as 2 (since x - 2 = 0 gives x = 2).
- Write down the coefficients of the dividend, which is 1x + 5. So, the coefficients are [1, 5].
- Set up a synthetic division bar:
```
2 | 1 5
|
```
2. Perform the Synthetic Division:
- Bring down the leading coefficient (1):
```
2 | 1 5
|
|____________
1
```
- Multiply the root (2) by the number just written below the line (1) and write the result under the next coefficient:
```
2 | 1 5
| 2
|____________
1
```
- Add this result to the next coefficient:
```
2 | 1 5
| 2
|____________
1 7
```
3. Interpret the Results:
- The number at the bottom row (1 in this case) represents the coefficient of the quotient term (x) with no remainder, since the dividend is a linear polynomial.
- The final number (7 in this case) is the constant term of the quotient.
Therefore, the quotient in polynomial form when you divide (1x + 5) by (x - 2) is x + 7.
So the correct answer is:
A. [tex]\(x + 7\)[/tex]
1. Set up the Synthetic Division:
- Identify the divisor (x - 2) and note its root as 2 (since x - 2 = 0 gives x = 2).
- Write down the coefficients of the dividend, which is 1x + 5. So, the coefficients are [1, 5].
- Set up a synthetic division bar:
```
2 | 1 5
|
```
2. Perform the Synthetic Division:
- Bring down the leading coefficient (1):
```
2 | 1 5
|
|____________
1
```
- Multiply the root (2) by the number just written below the line (1) and write the result under the next coefficient:
```
2 | 1 5
| 2
|____________
1
```
- Add this result to the next coefficient:
```
2 | 1 5
| 2
|____________
1 7
```
3. Interpret the Results:
- The number at the bottom row (1 in this case) represents the coefficient of the quotient term (x) with no remainder, since the dividend is a linear polynomial.
- The final number (7 in this case) is the constant term of the quotient.
Therefore, the quotient in polynomial form when you divide (1x + 5) by (x - 2) is x + 7.
So the correct answer is:
A. [tex]\(x + 7\)[/tex]
