Polynomials
An expression that can have constants, variables and exponents, that can be combined using addition, subtraction, multiplication and division, but:
• no division by a variable.
• a variable's exponents can only be 0,1,2,3,... etc.
• it can't have an infinite number of terms.
A polynomial can have constants, variables, and exponents (except division by a varible).
Monomial, Binomial, and trinomial...
The terms that cannot be combined is the amount of terms you have. You can have a lot of terms... but you can't have an infinite amount of terms.
Standard Form.S
Standard form can be the equation that is not expanded, or to the power of a number.
If in standard form, a problem can be 7,120. But expanded can be, 7,000 + 100 + 20.
If you write it in scientific notation, it will look:
If in standard form, a problem can be 7,120. But expanded can be, 7,000 + 100 + 20.
If you write it in scientific notation, it will look:
The bottom shows an example of standard form and expanded form.
In an equation...
In an equation, the expression on one side, and 0 on the other.
Exmaple: x² + 7 + 0.
In a polynomial...
The number with the highest degree goes furthest to the right, and goes downward by the degree.
Exmaple:
In an equation...
In an equation, the expression on one side, and 0 on the other.
Exmaple: x² + 7 + 0.
In a polynomial...
The number with the highest degree goes furthest to the right, and goes downward by the degree.
Exmaple:
Factor Form...
Start off with a video, click below!
As you can see above, the fine looking gentleman uses the zero power property. He has the equation = 0, and find the roots of the problem. For exmaple, if you have:
This can only be done if you have the polynomial in factored form.
Dividing Polynomials!
Long division, remainder theorem, and synthetic division. Each method is a quality use to figure out how to divide a polynomial.
Remainder Theorem:
Remainder Theorem:
- Definition of REMAINDER THEOREM. : a theorem in algebra: if f(x) is a polynomial in x then the remainder on dividing f(x) by x − a is f(a)
An exmaple would be...
**You can only find this out if you have the x value, it is used to evaluating polynomials**
Longggggggggggg division |
You need to use long division before you can evaluate the polynomial.
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