Multiplying Polynomials

A polynomial is a term that has at least one variable, a plus or minus sign, and at least two terms.  When multiplying Polynomials, we need to remember the exponent rules for multiplication: multiply the base and add the exponent. Distribute your terms to everything on the inside of the parentheses.  For two full length examples on how to do this, please click the links below. One is an example of multiplying polynomials and the other is what to do if you a polynomial expression to the third power. Enjoy!

http://www.educreations.com/lesson/view/multiplying-polynomials/13770520/?s=rq90dK&ref=app

http://www.educreations.com/lesson/view/binomial-cube/13770838/?s=zVmwt3&ref=app

Exponent Rules

Today we discussed the three exponent rules that everyone should know: the multiplication rule, the power rule, and the division rule.  When multiplying with exponents, we multiply the bases (big numbers) and add the exponents of like terms. When multiplying with exponents on the outside of parentheses, put your bases to the power of the outside exponent and multiply your exponents inside with the one outside. When dividing with exponents, divide the bases and subtract the exponents.

Note: if you get a negative exponent when dividing, change it to a positive exponent by putting it in the denominator.

To see video examples on how to use these three rules, click here:

http://www.educreations.com/lesson/view/multiplication-rule/13607398/?s=v2LhdR&ref=app
Multiplication Rule

http://www.educreations.com/lesson/view/power-rule/13607503/?s=KnSbkN&ref=app
Power rule

http://www.educreations.com/lesson/view/division-rule/13607615/?s=RBSuTS&ref=app
Division Rule

Simplifying with Imaginary Numbers

Imaginary numbers are slightly different than other variables. We know that i is the same thing as the square root of -1, which doesn't make any sense, so we leave it in the problem. But what if we see i to the second power? We plug in a -1 instead! Why is this important? Because we cannot have anything higher than i in the solution to a problem. Therefore, if we see i squared in a problem, we must change it to -1 instead and then simplify.

To see a few examples on how to simplify expressions with i in them, please click the link below:

http://www.educreations.com/lesson/view/simplifying-radicals/13379407/?s=5goBUq&ref=app

The quadratic formula and imaginary answers

W know that the quadratic formula is used to find the zeroes, or x-intercepts, of a parabol on a coordinate plane. However, not all parabolas have functions that cross the x-axis!  Therefore, when we solve these types of questions with the quadratic formula, we will get imaginary answers that contain the variable "i" meaning that the solutions are not truly existing on the coordinate plane.

For s full-length example on how to solve a quadratic formula problem using imaginary numbers, please click the link here:

http://www.educreations.com/lesson/view/quad-formula-imaginary/13379176/?s=EINdGl&ref=app