What is a polynomial?
The definition of a polynomial is an expression the has two or more algebraic terms, that is containing different powers with the same variable. A polynomial is many numbers that are grouped together to make an expression containing different numbers, variables and exponents, that you can either add, subtract, multiply or divide.
Vocabulary:
degree – The degree in an expression is the highest numbered exponent that is attached to a variable.
constant – A constant is a number that is on it’s own or a number that doesn’t have a variable next to it. Constants are usually found at the end of the expression.
coefficient – The coefficient is the number that is in front of a variable, and there can be more than one coefficient in and expression.
leading coefficient – A leading coefficient is the number that is at the front of the expression, the one that is “leading”.
binomial – A binomial is an expression that has two terms in it, joined together by an adding or subtracting sign.
trinomial – A trinomial is an expression that has three terms in it, joined together by an adding or subtraction sign.
monomial – A monomial is an expression that only had one term.
How to use algebra tiles:
Adding polynomial:
When you are adding polynomials you need to make sure that you are sorting your terms and simplifying to make it easier. When you are sorting you need to find all the like terms and put them together and add them up. Simplifying it means that if there are negatives and positive you need to cancel out the zero pairs to make the expression simpler.
Subtracting polynomials:
When you are subtracting polynomials you have to switch everything in the brackets to a the opposite of what it was (positive to a negative/negative to a positive). Once you switch all of them then you just do the equation like you normally would.
Multiplying polynomials:
When you are multiplying polynomials you use the distributive law. What that means is the number that is in front of the brackets gets multiplied by all the numbers that are in the brackets and if there are exponents you add them together.
Dividing polynomials:
When dividing polynomials you take the number that the expression is being divided by and divide each term by that number. You can write each one separately or you can do it how it is, but it is easier to follow when you do each one individually. When you divide, you have to subtract the exponents attached to the terms, if there are any.
Connections to previous units:
One of the connections that I made in this unit to previous units is the exponent laws from the rational numbers unit. We learned the four laws that helped us determine what to do with the exponents and you have to use the multiplication and division laws for polynomials. When you are multiplying polynomials you use the multiplication law because you are adding the exponents and when you are dividing polynomials you are using the division law because you are subtracting the exponents.