What I Learned About Grade 9 Polynomials
What is a polynomial?
A polynomial is four or more terms even though in this unit we are considering Monomials which is one algebraic term, Binomials which is two, and Trinomials being three all under the Polynomial title .
Vocabulary
Degree- The degree of the polynomial is the highest exponent on the term. The thing you have to remember is that the degree is only on the variable in the equation
Constant- The constant is the number in the term that does not have a variable in front of it. It is called the constant because in the equation whatever the variable means the number will stay the same since there is no variable attached.
Coefficient- The coefficient is the number infront of the variable, In the polynomials it is the amount of the type of variable.
Leading Coefficient- the leading coefficient is just the first number in the term that also has a variable behind it.
Monomial- A monomial is the equation with numbers and letters that only has one term
Binomial- A Binomial is the equation with numbers and letter that has 2 terms instead of 1 so you have to simplify it by adding and or subtracting the 2.
Trinomial- A trinomial is the exact same explanation as the Monomial and Binomial except this has 3 terms instead of the previous 2 and 1 terms.
How to Use Algebra Tiles
the big square Is the variable squared. The rectangle is just a normal variable. The small square is just 1.
This is the question all put out into blocks. I know it is a bad picture but the equation is 4x squared – 2x + 1 – 2x squared + 9x – 3
all of the upside down or white tiles mean that is is the same as the coloured ones except negative
After that you want to pair it up so you have the equation in alphabetical order
next you want to deduct the negatives from the equation so for every negative of the type you see you take that one away and you take a positive one away too. Same with the other way around.
the answer is …
Add Polynomials
Adding polynomials, to add polynomials you first have to analyze and see how many different variables there are and then what they are. After that you add the ones that have the same variables until there are no more to add. Then you write your answer in an organized way. (typically alphabetical order left to right, with the bigger exponent numbers farther to the left.
Subtract Polynomials
Subtracting polynomials, It is very similar to adding them. The first step is again analyzing which variables there are and grouping them. Secondly you subtract the ones that have the same variable and then organize it the exact same way that you would for the addition ones.
Multiply Polynomials (Distributive)
Multiplying polynomials is actually quite easy. Starting it off, if you are doing it with just a basic number like 2 to multiply with then, you multiply it just as you normally would multiply but then remember to keep the same variables on and organize it for the answer. However, if you multiply it with a number that has a variable like 2x, then you do the same multiplication but on all of the answers you add a x for the variable. If the question had for example 11x and you had to times it by 2x then it would be 22x to the second power, since there are 2 x`s.
Divide Polynomials
Dividing the polynomials is quite similar to the multiplication. When you do the division with an ordinary number like 4 then you just divide the numbers as you normally would. But when you are doing it with a variable like 4x then when you divide the numbers that have a variable you divide them as you normally would but you also take away one of the x`s . It is basically the exact opposite of multiplication
Making Connections to Previous Units
The biggest connection to previous units would be exponents. Specifically the power law, you use the power law during multiplication and division just the same as we did in the last unit.