## Dividing Polynomials: (x^3-5x^2-33x-35) ÷ (x+3)

This article will guide you through the process of dividing the polynomial (x^3-5x^2-33x-35) by (x+3) using polynomial long division.

### Understanding Polynomial Long Division

Polynomial long division is similar to long division with numbers. We'll be using the following steps:

**Set up:**Arrange the polynomials in descending order of their exponents.**Divide:**Divide the leading term of the dividend by the leading term of the divisor. Write the result above the dividend.**Multiply:**Multiply the result by the divisor and write the product below the dividend.**Subtract:**Subtract the product from the dividend.**Bring down:**Bring down the next term of the dividend.**Repeat:**Repeat steps 2-5 until you reach a remainder that is either zero or has a degree less than the divisor.

### The Division Process

Let's perform the long division:

```
x^2 - 8x - 9
x+3 | x^3 - 5x^2 - 33x - 35
-(x^3 + 3x^2)
-----------------
-8x^2 - 33x
-(-8x^2 - 24x)
-----------------
-9x - 35
-(-9x - 27)
-----------------
-8
```

### Result and Interpretation

From the division, we find that:

**Quotient:**x^2 - 8x - 9**Remainder:**-8

Therefore, the division of (x^3-5x^2-33x-35) by (x+3) can be expressed as:

**(x^3-5x^2-33x-35) ÷ (x+3) = x^2 - 8x - 9 - 8/(x+3)**

This means that (x^3-5x^2-33x-35) is equal to (x+3) multiplied by (x^2 - 8x - 9) with a remainder of -8.