What I Have Learned about Grade 9 Polynomials
What is a polynomial?
A polynomial is where you get all the algebraic terms like subtraction, addition, multiplication, division. There is also a key part we were missing and that’s the variables ex. 2x(x+5) this is one example of a polynomial. So many terms fit into a polynomial (fractions, coefficient, constant) and we will be talking about them in the next section.
Vocabulary :
Degree: A degree is the number of an exponent on the variable for example with the number 5x to the 4 power, and 5x to the 2
the degree for that one would be 4 (which ever one is higher exponent that would be the degree)
Constant: The constant in a polynomial is where the number is all by it self, it had no variables in it nor a power. Its usually at the end of the equations.
Coefficient: Is where there is a variable, its similar to a constant but just one thing changed. for example you would have to put the number in front, ex. 7x this would be a coefficient and the answer would be 7.
Leading coefficient: The leading coefficient is where its leading the equation, to it would start you off. in that case the leading coefficient would be the first number in the equation.
Monomial: is where there’s one term and only one term ex. -2x
Binomial: Is where there’s two terms in one equation ex. -2x+ 3
Trinomial: “Tri” stands for three so trinomial is where there’s three terms in one equation ex. -2x+ 3- 5x(squared)
Add polynomials/ Subtract polynomials:
Adding and subtracting polynomials is really nice.Because, you get to use the algebra tiles and when using the algebra tiles the equation get easier. There is also another way to make it simple, you would just group them together (all the like terms) and you would do the equation when you group them for example the equation here
ex.
When you are subtracting polynomials the sings flip, it doesn’t flip in the beginning it flips after the minus sign. Like what I have done in this photo
as you can see you could add the algebra tiles to show your work.
Multiply polynomials:
for multiplying polynomials there is really one way that works for me and its the distributive property. The distributive property is where you take the number outside of the brackets, and you multiply EACH number inside the brackets. for example this equation here
ex.
Divide polynomials:
The high school way of dividing polynomials is really like the other unit we have done with the fractions, so you would just make it into a huge fraction and divide it. Their also different steps for the exponents as well, you don’t divide the exponents you subtract them in stead.
ex.
Make connections to previous units:
in the previous units we have done a huge fraction where you take everything and divide it with the number from the bottom, so that connects to the fractions unit. But also for the rational numbers unit we learned about negative and positive numbers and how we subtract, add, multiply, and divide them. Know in this unit we added exponents with variables!