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

On thursdsay, March20th in PRECAL20s the only thing we did for notes was:
Example:Factor
xsquared-4x-12
=(x+2)(x-6)

xsquared+6x-16
=(x+8)(x-2)

xsquared+1-20
=(x+5)(x-4)

There were two assignments handed out on thursday they were PAGE:120,37-44, and the class had to finish the rest of the orange booklet.

Thise post was added by Dustin G. Woods

March 18/08

Today March 18/2008 in pre cal 20s we learned how to do factoring.
Factoring:
We now begin a discussion of the algebraic operation called factoring. Factoring an expression is to rewrite the expression entirely as a polynomial product.
Factoring Over the Integer:
A polynomial is considered completely factored when there are no more variable factors can be removed. No more integer factor, other than 1 or -1 can be removed. The steps for this process is 1. find the GCF (greatest common factor). 2. What is the GCF of the coefficients (exponents)? 3. What is the GCF of the variables (letters)? 4. Check: Multiply and see if you get the same expression that you started with.
Factoring by Grouping?
Some polynomials do not have a common factor in all their terms. These polynomials can sometimes be factored by grouping terms that do have a common factor.
The assignments we had assigned to us today are: page 120 #11-22 and page 120 #30-36

Products of a Monomial and a Polynomial -March 12

Today in class we learnt how to multiply monomials and polynomials. Basically all you have to do is multiply the monomial outside of the brackets by the polynomial inside the brackets.
Ex: Expand
3a(4a-3b)
=12a²-9ab

We also learnt how to simplify these expressions. To simplify an expression you, first, expand the expression like we have already done and then, secondly, collect like terms.
Ex: Expand and Simplify
4x(2x²+ 5x -3) –(2x²-7)
=8x³+20x²-12x-2x²+7
=8x³+18x²-12x+7

The final thing that we learnt to do today was multiplying binomials. When multiplying binomials you use the F.O.I.L. method. The F.O.I.L. method stands for multiplying the First two terms, then multiplying the Outside two terms, then multiplying the Inside two terms, and, finally, multiplying the Last two terms.
Ex: Find the product of the binomials
(x+6)(x+8)
=x²+8x+6x +48 <----(F.O.I.L. method)
=x²+14x+48 <----( you have to collect like terms here too.)

The assignment for today was:
pg.107, questions 1-29 odd and pg.108, questions 32-43 and 45-67