Dividing (x3-6x2+9x+3) by (x-1)

When dividing a polynomial by a linear factor, we use the method of long division. Before we begin, we need to make sure that the terms in the dividend are arranged in descending order of their exponents.

The Long Division Method

The long division method involves the following steps:

1. Divide the first term of the dividend by the divisor and write the result on the top of the division symbol.

2. Multiply the divisor by the quotient just obtained and write the result underneath the first two terms of the dividend.

3. Subtract the result obtained in step 2 from the first two terms of the dividend. Bring down the next term from the dividend to the resulting polynomial.

4. Repeat steps 1-3 until no more terms are left in the dividend or the degree of the remainder is less than the degree of the divisor.

Dividing (x3-6x2+9x+3) by (x-1)

Now let's apply the long division method to divide (x3-6x2+9x+3) by (x-1):

```
x^2 - 5x + 4
-------------------
x - 1 | x^3 - 6x^2 + 9x + 3
x^3 - x^2
----------
-5x^2 + 9x
-5x^2 + 5x
----------
4x + 3
```

Therefore, (x3-6x2+9x+3) divided by (x-1) equals x^2 - 5x + 4 with a remainder of 4x + 3.

Conclusion

In conclusion, when dividing a polynomial by a linear factor, we use the method of long division. The answer is obtained by dividing the first term of the dividend by the divisor and writing the result on the top of the division symbol. The divisor is then multiplied by the quotient just obtained and subtracted from the first two terms of the dividend. The process is repeated until no more terms are left in the dividend or the degree of the remainder is less than the degree of the divisor.

x^2-5x+4 with remainder 7