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example
x5 + 6x4 + 9x3
To factor this expression, see if each "piece" of the expression has a variable in common. In this case, each piece has an X in common.
Now we factor out the smallest exponent of X that we see in the expression.
x3(x2+6x +9)
You could factor the x squared +6x +9 also, into (x + 3)(x+3)
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How did we use hypatia's discovery today?
We use letters called variables in mathematical form. Before we did not know anything about variables, thats why it was harder.
How many variables can be tested in an experiment?
1
Type of graph that compares variables with one variable divided into parts?
bar
What was the deciding factor in the Vietnam war?
SACs B52 Stratofortress was the deciding factor.
What is a contributing factor of the war of 1812?
A factor was that the British navy was seizing us cargo.
Are there variables in exponents?
In algebraic equations, exponents can contain variables. They can be solved for by using logarithmic rules for exponents.
How do you find the greatest common factor of variables?
Choose the lowest of the exponents. The GCF of x3 and x5 is x3
What is the sum of the exponents of the variables of a monomial is the of the monomial?
The degree of a term is the sum of the exponents on the variables.
When subtracting what to do with the exponents?
It depends on whether you are working with variables. You cannot add terms with variables that have unlike exponents.
How do you subtract like variables with different exponents?
You can't. You can only subtract like terms. Like terms must have exactly the same variables and exponents on the variables.
When dividing variables with exponents subtract exponents?
Yes. When you divide one variable with an exponent from another, you subtract the exponents
When multiplying 2 or more variables with exponents what do you do with the exponents?
You add the exponents- x^2*x^6=x^8
If two exponents have the same factor or base what happens to the exponents when the exponents are multipled?
The exponents are added.
When adding variables with exponents do you add or subtract the exponents?
When adding variables with exponents, you do neither. You only add the exponents if #1 The variables are the same character (such as they are both "a") #2 You are multiplying the variables (NOT ADDING, SUBTRACTING, OR DIVIDING) Using a simple concrete case may make this clearer: 10+2 times 10+3 equals 10+5 ( 100 times 1000 equals 100,000).
What is The sum of the exponents on the variables in a term?
Degree of a Polynomial
When multiplying variables with the same base what do you do with the exponents?
You add them.
What does it mean if a function is a polynomial?
It means that it has constants and variables that has a form of something like 7x2+2x+5 or something like that. Variables can not be used as exponents though, and exponents have to be whole numbers. Also, variables can not be a denominator.
