Polynomials

What is a polynomial:

A polynomial is a question that has a variable and coefficient, it also had adding, subtracting,                                                                     multiplication and division. some question also have exponents.                                                                                                                             example:    ,                 

Vocabulary (degree, constant, coefficient, leading coefficient, binomial, trinomial and monomial)

The degree of a polynomial is the highest degree of its monomials with non zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it and thus is a non-negative integer.
A constant term is a term in an algebraic expression that has a value that is constant or cannot change
A coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression
The leading coefficient in a polynomial is the coefficient of the leading term. In this case, the leading term is and the leading coefficient is
A binomial is a polynomial that is the sum of two terms, each of which is a monomial. It is the simplest kind of polynomial after the monomials.
Trinomials are the algebraic expression with three unlike terms, hence the name Trinomial.
Monomials are the algebraic expression with one term, hence the name says Monomial.

 

Adding polynomials 

for me adding was easiest all you have to do is add the leading coefficient, but when there are variables then you would add the variables together for example let’s say there was an question that showed that 2x plus 3x all you would do is add the 3 and the 2 and that would equal 5x that’s the beginning of adding after words it gets harder the questions start to have exponents so let me give another example there is a question that shows 3x to the power or 2 plus 4x to the power of 2 all you would do is add the 3 and the 4 which equals to 7 you put the x in it and just keep the two how it is so your left with 7x to the power of 2

Subtract polynomials

This is the second easiest out of the polynomial unit. You are only subtracting the variable so let me give you an example let’s say there is a question that shows 6m subtract from 4m all you would do is subtract the 6 from the 4 so the answer would be 2m. if you are subtracting with exponents then you would not change anything so let me give you another example lets say there is a question that shows 5m to the power of 5 subtract from 3m to the power of 3 all you would d is subtract the 5 and the 3 and you would keep the exponents the same you the answer would be 2m to the power of 3.

Multiply polynomials (distributive)

When multiplying polynomials it is very different from adding or subtracting polynomials so lets me give you an example of the basic of multiplying polynomials so here’s and example 6m times 7m so all you do is multiply the 6 and the 7 so that would be 42 but you need to know that every variable has a invisible 1 so if you look and the question there are 2 m so that mean that there are 2 invisible 1 so you add the two 1 and that makes 2 so they whole answer would be 42m square you could also write it as 42m to the power 2 so its not that hard, you also need to remember that you can also write a multiplication question written this way 2 (2m + 3m) so you would do 2 times 2 which would be 4 and then you would do 3 times 2 which would be 6 so then you would do 4m + 6m and all you do is add

Dividing polynomials

When dividing polynomials it is like when you dividing two numbers together so let me give you an example 6m divide 3m so you would do 6 divide by 3 which would be 2 and all you do is put the m with it but when the m has a variable in it then it is different for example 10x to the power of 3 divide 2x to the power of 2 so you would subtract the two exponents and just divide the two numbers so your answer would be 2x to the power of 1.

Make connections to previous units (exponents and rationales)

I made a few connection but the mane thing I noticed when I was doing do the polynomial is that there are a lot of exponents in this unit so it was much easier another thing that I noticed when I was doing polynomials is that when there is a question that is a little bit harder there are brackets so you need know BEDMAS so you need to do brackets first then exponents and so on so it was really good that we learned all this before we started the polynomial unit.

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