Sunday, March 23, 2008

Monomials and Polynomials

In PreCal20S, on March 11th,
we learnt that Monomials are:
- A number
- A product of one or more variables
- The product of a number and one or more variables

Monomials consist of a numerical coefficient and a variable.

Polynomials

Are algebraic expressions formed by adding or subtracting monomials.
Each monomial is a term of the polynomial.

x + 17
Binomial = two terms

x² + 4x - 3
Trinomial = three terms

Evaluating Polynomials
Evaluate the expression for the given value of the variable:
x² + 4x - 3 for x = 2

= (2)² + 4(2) -3

= 4 + 8 - 3

= 9

Mathematical Convention

The terms of a polynomial are usually written so that the exponents of the variable are in descending order or ascending order.

If there is more than one variable, then it is written in ascending or descending order of one od the variables.

Ex. Write the polynomial in ascending order of x :

5x³y + 4xy³ -3 + 4x²y²

= -3 + 4xy² + 4x²y² + 5x³y

Adding Polynomials

(x² + 4x - 2) + (2x² -6x +9)

= x² + 2x² + 4x - 6x -2 +9
= 3x² - 2x + 7

OR

x² + 4x - 2
+ 2x² - 6x + 9
_____________
= 3x² - 2x +7

Subtracting Polynomials

(6a² - ab + 4) - (7a² + 4ab - 2)
= 6a² - 7a² - ab + 4ab + 4 - 2
= -a² + 5ab + 2

OR

4y² - 2y + 3
- (3y² + 5y -2)
___________
= y² - 7y + 5

And for our assignment we just finished off the math booklet.

Taylor Wigston

2 comments:

Nicole L. (Mentor) University of Regina said...

This was a great entry. I liked that you used both definitions and examples. I only have two small tips.
First, while I was able to follow your examples quite easily, some people might benefit from a brief written description of the steps.
My second tip is getting really finicky, so you must be doing a good job to make me reach this far for advice! Just watch that your formatting is consistent. You bolded and underlined main ideas, and this really helped to organize this post, but if you are going to italicize one of your definitions, make sure you italicize them all. In fact, your class may want to decide on a way to keep formatting consistent, even from scribe to scribe; if you all agree to italicize all definitions of terms, then the entire blog will be more consistent, and therefore an easier resource to follow.

Nicole L. (Mentor) University of Regina
Email: little1n@uregina.ca
Blog: http://nicolelittle.wordpress.com

Ste. Anne Collegiate - PreCal 20S 2008 said...

Good Job Taylor! Mrs. Remple