# Quick Math Polynomial Division- Division

## Quick Math Polynomial Division

1
##### Enter expression in this form

Example: 2x^3 + 3x^2 - 5x + 6 , x - 1

The dividend and divisor are separated by comma.

### Polynomial Division of Algebraic Expressions

Polynomial division is a process similar to long division with numbers, but it involves polynomials. When dividing polynomials, we typically use the long division method or synthetic division (if the divisor is a binomial of the form $$x – c$$). Here, we’ll focus on the long division method.

#### Steps for Polynomial Long Division:

1. Arrange: Write both the dividend and the divisor in descending order of their degrees.
2. Divide: Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
3. Multiply: Multiply the entire divisor by the first term of the quotient.
4. Subtract: Subtract the result from the dividend to form a new polynomial.
5. Repeat: Repeat the process using the new polynomial as the dividend until the degree of the remainder is less than the degree of the divisor.

#### Detailed Example:

Let’s divide $$2x^3 + 3x^2 – 5x + 6$$ by $$x – 1$$.

1. Arrange the polynomials:
– Dividend: $$2x^3 + 3x^2 – 5x + 6$$
– Divisor: $$x – 1$$

2. Divide the first term:
– $$\frac{2x^3}{x} = 2x^2$$
– Quotient: $$2x^2$$

3. Multiply:
– $$2x^2 \cdot (x – 1) = 2x^3 – 2x^2$$

4. Subtract:
$(2x^3 + 3x^2 – 5x + 6) – (2x^3 – 2x^2) = 3x^2 – (-2x^2) – 5x + 6 = 5x^2 – 5x + 6$

5. Repeat the process with the new dividend $$5x^2 – 5x + 6$$:
– $$\frac{5x^2}{x} = 5x$$
– Quotient: $$2x^2 + 5x$$
– Multiply: $$5x \cdot (x – 1) = 5x^2 – 5x$$
– Subtract:
$(5x^2 – 5x + 6) – (5x^2 – 5x) = 6$

6. Final Step:
– New dividend: $$6$$
– Since the degree of the remainder (0) is less than the degree of the divisor (1), the division process stops.

The final quotient is $$2x^2 + 5x + 1$$ and the remainder is $$7$$.

So,
$\frac{2x^3 + 3x^2 – 5x + 6}{x – 1} = 2x^2 + 5x + 1 + \frac{7}{x – 1}$