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Multiplication of Polynomials

Multiplication of Polynomials

Author: Sara Gorsuch
Description:

This packet will show you how to multiply polynomials and how to use the FOIL system.

I will go over to remind exactly what polynomials are and what you do with them, go over what foiling is,and an examples of multiplying regular polynomials and then multiplying two binomials using foiling!

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Tutorial

Review of What Exactly a Polynomial Is.

  Polynomial: is just an expression that has a bunch of variable or constant terms in them that are raised to non-zero exponents.

Remember: No polynomial has a negative or fractional exponent or a root sign within the expression, if it does it is NOT a polynomial. 

Polynomial Termonology:

Degree: This is the highest exponent in the polynomial, look to the highest exponent and that will define the degree of the polynomial. 

Example: 4x4+5x2=18 as you see in this expression the highest exponent is a 4th, so the polynomial

would be defined as a 4th degree polynomial. 

(eventually in polynomials you will want to find what x is, the degrees will eventually tell you how many answers there are to x, so if there is for example 4x2+8x+25 there will be two values for x)

Standard Form Polynomial: With a polynomial the standard form is when the expression is put in order from the largest to the smallest exponents, then to basic variables and then to the constants(numbers)                                                          

 Example: 5x8+3x4-7x+4 this is standard form because as you see, first is the largest exponent then the

next largest, next the basic variable and then the constant(number).

What do you do with polynomials? Well, you need to learn how to simplify them using multiplication, addition, subtracting and division. This will lead into factoring them and solving for x. Also, a bit of graphing. 

Who even uses polynomials in real life? What kind of jobs uses this stuff?

Fields relating to architecture, agriculture, engineering fields such as electrical and civil engineering and various other science related jobs. Even people with regular business jobs use polynomials! It is even used in our regular finances!

Foiling

  keep this in mind in mind: you can ONLY use it for the special case of multiplying two binomials. You can NOT use it at ANY other time! 

Foiling tells us this, you multiply the first terms, then the outer terms, then the inner and finally the last!

Example Problems.

Includes multiplying polynomials and using foiling. (The second example shows that you do not even have to use foiling to multiply two binomials)