What is a polynomial

A polynomial is an expression, made from variables and coefficient. Variables can be showen as letters to separate them from the numbers.

Vocabulary

Degree-The degree is the biggest exponent in the expression.

Constant-The constant term is the term that does not change, if the variable changes.

Coefficient-The coefficient is a number quantity placed before and multiplying the variable in an algebraic expression, like (4 in 4x2)

Binomial-A binomial is an expression with two Coefficients. For example (5x+3)

Trinomial-A Trinomial is also an expression about, but except of two coefficients, there is three. So in stead of (5x+3) a Trinomial looks like (2x2+3x-8)

Monomial-For monomial it is only one like (6x)

How to use algebra tiles

Adding polynomials

When adding polynomials, you have to organize all the numbers that have like terms. When you have them grouped, then you just simply add the coefficients together.

8x+4+3x+2x+7

8x+3x+2x           4+7

=13x+11

Subtracting polynomials

When subtracting, do the same thing as with adding but after sorting just subtract instead. But if you have a bigger number subtracting from a smaller number you will have to go into the negatives. ( It becomes negative, you have to switch out the plus sign for a subtract sign)

8x-4-3x-2x-7

8x-3x-2x           4-7

=3x-3

Multiplying polynomials (distributive)

When multiplying, it will look something like this   5(3x+4)   but when you multiply, you will writ it out as 5×3x  and  5×4. Then will end up with 15x+20. But if you have something like   2x+5(3x+4)   you will have to multiply the numbers with like terms, like in adding and subtracting.   (2x)(3x)   and    (5)(4)   = 6x+20

If you have an exponent on the multiplier and none on the bottom, it will change the exponents on the variable. I there is a exponent on both then you add the two exponents together. (Remember if there is just a variable and no exponent, then the exponent is 1)

Dividing polynomials

when dividing polynomials I like to write mine out as a fraction like   \frac{6x+4}{2}   whereyou have to start off by spitting the top part in half   \frac{6x}{2}   and   \frac{4}{2}   then divide and after you will put the two results together.   \frac{6x}{2}   and   \frac{4}{2}   =   3x+2

If you have an exponent on the numerator and none on the bottom, it stays the same. If there is a exponent on both then you subtract the denominators exponent from the numerators.

Connections from Previous Units (Exponents and Rationals)

In this unit we used different concepts from the beginning of the year that we did during this. Like in our exponents unit we learned all about them so when it came to this unit we knew what we needed to do with them.