Division of Polynomials

I.  Homework

II.  Dividing by a Monomial

To divide a polynomial by a monomial, we can divide each term ty the monomial.

Example:

(4x² - 2x  - 3)/(5x) = 4x²/(5x) - 2x/(5x) - 3/(5x)

= 4x/5 - 2/5 -3/(5x)

Exercises:

A.  (2x³ +5x² - 4)/(3x)

B.  (7x⁴ -3x² + x - 2)/(6x² )

II.   Polynomial Division

Recall how to perform long division:  

We will divide 1236 by 9.

We see that we follow the steps:

1)  Write it in long division form.

2)  Determine what we need to multiply the quotient by to get the first term.

3)  Place that number on top of the long division sign.

4)  Multiply that number by the quotient and place the product below.

5)  Subtract

6)  repeat the process until the degree of the difference is smaller than the degree of the quotient.

Write as sum of the top numbers + remainder/quotient.

We will do the following examples:

A)  (3x² + 5x + 7)/(x + 1)

B)  (2x⁴ + x - 1)/(x² + 3x + 1)