This week in math 10 we finished our trigonometry unit and started our polynomial unit by reviewing what we learned in grade 9 about polynomials. I believe the most important thing I learned and reviewed this week was how to add, subtract, divide and multiply polynomials. This is important to me because as I start to do more complicated equations with polynomials knowing the basics will help insure silly mistakes are not made.

 

Adding Polynomials: ex (5x^3)+(7xy)+(4x^3)

When adding polynomials firstly you should arrange the terms in a horizontal line.

5x^3+7xy+4x^3

Next you should group terms with the same variables together.

5x^3+4x^3+7xy

And then you can add all the terms that have the same variables as each other together.

5x^3+4x^3+7xy= 9x^3+7xy

 

Subtracting Polynomials: ex (6x-5y)-(8x)

Subtracting and adding polynomials are very similar in the sense that you can only subtract polynomial terms with the same variables.

(6x-5y)-(8x) becomes 6x-5y-8x because the negative sign needs to be multiplied to the (8x)

Then because 6x and -8x have the same variable you can subtract them.

6x-5y-8x= -2x-5y

 

Multiplying Polynomials:

When multiplying polynomials you have to follow the F.O.I.L. (first, outer, inner, last) rule and the distribution law. Each term needs to be properly distributed when multiplying polynomials or else the answer will not be correct.

ex:(3x+2)(5x+6)

These are the first terms (3x)(5x)=15x^2

These are the outer terms (3x)(6)=18x

These are the inner terms 2(5x)=10x

These are the last terms 2(6)=12

Once the terms have been distributed you can add the terms with the same variables.

15x^2+18x+10x+12=15x^2+28x+12

 

Dividing Polynomials:

ex: 40x^3+10x-5x^2/5x

The first step to divide polynomials is to arrange them in descending order of there degree.

40x^3+10x-5x^2/5x

=40x^3-5x^2+10x/5x

The next step is to divide each numerator term by the denominator and simplify each answer.

40x^3/5x=8x^2

-5x^2/5x=-x

10x/5x=2

40x^3+10x-5x^2/5x=8x^2-x+2

Example #1

Example #2