ThatQuiz Test Library Take this test now
Lesson Rational Root Theorum
Contributed by: Pappal
 A rational number is
 A rational number is
a number that can be turned into a fraction
 A rational number is
2 is rational
a number that can be turned into a fraction
 A rational number is
2 is rational
because it could be turned into
a number that can be turned into a fraction
2
1
 A rational number is
0.5 is rational
2 is rational
because it could be turned into
a number that can be turned into a fraction
2
1
 A rational number is
0.5 is rational
2 is rational
because it could be turned into
a number that can be turned into a fraction
because it could be turned into
1
2
2
1
In general, rational numbers are anything BUT
In general, rational numbers are anything BUT
square roots
In general, rational numbers are anything BUT
So √2 is not rational
square roots
In general, rational numbers are anything BUT
So √2 is not rational
but √4 is
square roots
In general, rational numbers are anything BUT
So √2 is not rational
but √4 is
square roots
because it equal 2
√5
.23
Irrational
?
Rational
?
A 'root' is an answer to a polynomial equation
A 'root' is an answer to a polynomial equation
x2 - 2x - 3 = 0
A 'root' is an answer to a polynomial equation
x2 - 2x - 3 = 0
This is a polynomial
A 'root' is an answer to a polynomial equation
x2 - 2x - 3 = 0
This is a polynomial
the equal sign makes
this an equation
A 'root' is an answer to a polynomial equation
x2 - 2x - 3 = 0
So this is a polynomial equation
The answers to this equation are 3 and -1
A 'root' is an answer to a polynomial equation
x2 - 2x - 3 = 0
The answers to this equation are 3 and -1
A 'root' is an answer to a polynomial equation
these are also called
x2 - 2x - 3 = 0
The answers to this equation are 3 and -1
A 'root' is an answer to a polynomial equation
these are also called
x2 - 2x - 3 = 0
the roots
The answers to this equation are 3 and -1
The reason it is called 'roots' is complicated
A 'root' is an answer to a polynomial equation
these are also called
x2 - 2x - 3 = 0
the roots
The answers to this equation are 3 and -1
The reason it is called 'roots' is complicated
A 'root' is an answer to a polynomial equation
but it has to do with the idea that the solution
these are also called
x2 - 2x - 3 = 0
the roots
The answers to this equation are 3 and -1
The reason it is called 'roots' is complicated
A 'root' is an answer to a polynomial equation
but it has to do with the idea that the solution
these are also called
to the equation x2=9
x2 - 2x - 3 = 0
the roots
The answers to this equation are 3 and -1
The reason it is called 'roots' is complicated
A 'root' is an answer to a polynomial equation
but it has to do with the idea that the solution
these are also called
to the equation x2=9
would be the square ROOTS of 9 (3 and -3)
x2 - 2x - 3 = 0
the roots
The answers to this equation are 3 and -1
The reason it is called 'roots' is complicated
A 'root' is an answer to a polynomial equation
but it has to do with the idea that the solution
these are also called
to the equation x2=9
would be the square ROOTS of 9 (3 and -3)
x2 - 2x - 3 = 0
the roots
and so the answers could be called roots as well
The roots/answers/solutions also happen to be
The roots/answers/solutions also happen to be
the x-intercepts
We already meantioned that the roots of 
The roots/answers/solutions also happen to be
the x-intercepts
x2 - 2x - 3 = 0
We already meantioned that the roots of 
The roots/answers/solutions also happen to be
the x-intercepts
x2 - 2x - 3 = 0
are 3 and -1
We already meantioned that the roots of 
The roots/answers/solutions also happen to be
the x-intercepts
x2 - 2x - 3 = 0
are 3 and -1
the x intercepts
We already meantioned that the roots of 
The roots/answers/solutions also happen to be
the x-intercepts
x2 - 2x - 3 = 0
are 3 and -1
the x intercepts
We already meantioned that the roots of 
The roots/answers/solutions also happen to be
the x-intercepts
x2 - 2x - 3 = 0
are 3 and -1
the x intercepts
We already meantioned that the roots of 
The roots/answers/solutions also happen to be
are also 3 and -1
the x-intercepts
x2 - 2x - 3 = 0
are 3 and -1
Answer listed smallest to largest with comma and space betweeneach answer (e.g. -4, 12)
The roots are
The rational root theorum gives us a list
The rational root theorum gives us a list
of all the possible rational roots
The rational root theorum gives us a list
of all the possible rational roots
of a polynomial
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
of all the possible rational roots
of a polynomial
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
of all the possible rational roots
of a polynomial
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
of all the possible rational roots
of a polynomial
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
of all the possible rational roots
of a polynomial
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
of all the possible rational roots
of a polynomial
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
of all the possible rational roots
of a polynomial
1
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
of all the possible rational roots
of a polynomial
1
7
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
of a polynomial
1
7
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
of a polynomial
1
7
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
of a polynomial
1
1
7
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
of a polynomial
1
1
7
5
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
then write all the possible combinations
of a polynomial
1
1
7
5
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
then write all the possible combinations
of a polynomial
1, 
1
1
7
5
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
then write all the possible combinations
of a polynomial
1, 1/5, 
1
1
7
5
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
then write all the possible combinations
of a polynomial
1, 1/5, 7, 
1
1
7
5
write all the factors of the last number
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
write a fraction bar
then write all the factors of the first number
of all the possible rational roots
then write all the possible combinations
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5, +7
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5, +7, +7/5
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5, +7, +7/5, -1
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5, +7, +7/5, -1, -1/5
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5, +7, +7/5, -1, -1/5, -7
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Given the polynomial 5x3-7x2-5x+7
The rational root theorum gives us a list
So the list of possible rational roots is
of all the possible rational roots
+1, +1/5, +7, +7/5, -1, -1/5, -7, -7/5
of a polynomial
1, 1/5, 7, 7/5
1
1
7
5
Factors of 8
1, 
, 4 ,
3x3 -5x2 +x -4
Factors of 4
?
Factors of 3
?
3x3 -5x2 +x -4
1, 2, 4
?
1, 3
?
Factors of 4
Factors of 3
How do we know which numbers on the list
How do we know which numbers on the list
are actually answers/roots/solutions?
There are three ways.
How do we know which numbers on the list
are actually answers/roots/solutions?
There are three ways.
How do we know which numbers on the list
Plug In
are actually answers/roots/solutions?
There are three ways.
How do we know which numbers on the list
Plug In
Divide
are actually answers/roots/solutions?
There are three ways.
How do we know which numbers on the list
Plug In
Divide
Graph
are actually answers/roots/solutions?
Using the polynomial 3x3 +13x2 +13x +3
Using the polynomial 3x3 +13x2 +13x +3
let's find the list of rational roots
Using the polynomial 3x3 +13x2 +13x +3
let's find the list of rational roots
and see which ones actally work
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
=
+1, 
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
=
+1, +1/3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
Already got a '1'
let's find the list of rational roots
and see which ones actally work
=
+1, +1/3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
=
+1, +1/3, +3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
=
+1, +1/3, +3, -1, -1/3, -3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Let's see if -1 works by plugging it in for x
=
+1, +1/3, +3, -1, -1/3, -3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Let's see if -1 works by plugging it in for x
=
3x3+13x2 +13x +3
+1, +1/3, +3, -1, -1/3, -3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Let's see if -1 works by plugging it in for x
=
3x3+13x2 +13x +3
3(-1)3+13(-1)2+13(-1)+3
+1, +1/3, +3, -1, -1/3, -3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Let's see if -1 works by plugging it in for x
=
3x3+13x2 +13x +3
3(-1)3+13(-1)2+13(-1)+3
+1, +1/3, +3, -1, -1/3, -3
-3+13-13+3 = 0
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Let's see if -1 works by plugging it in for x
=
3x3+13x2 +13x +3
3(-1)3+13(-1)2+13(-1)+3
+1, +1/3, +3, -1, -1/3, -3
-3+13-13+3 = 0
it works
It equals
zero so
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
=
+1, +1/3, +3, -1, -1/3, -3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
=
13
+1, +1/3, +3, -1, -1/3, -3
13
3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
3
=
13
+1, +1/3, +3, -1, -1/3, -3
13
3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
3
=
13
-3
+1, +1/3, +3, -1, -1/3, -3
13
3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
3
=
13
10
-3
+1, +1/3, +3, -1, -1/3, -3
13
3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
3
=
13
10
-3
+1, +1/3, +3, -1, -1/3, -3
13
-10
3
3
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
3
=
13
10
-3
+1, +1/3, +3, -1, -1/3, -3
13
-10
3
-3
3
0
Using the polynomial 3x3 +13x2 +13x +3
1    3
1    3
-1
let's find the list of rational roots
and see which ones actally work
Now let's see if -1 works by dividing
3
3
=
13
10
-3
+1, +1/3, +3, -1, -1/3, -3
13
-10
3
-3
3
0
The remainder
so it works
is zero 
Now let's see if it works by graphing
Now let's see if it works by graphing
3x3+13x2 +13x +3
1
-1
2
-2
1
-1
2
-2
3
-3
Now let's see if it works by graphing
3x3+13x2 +13x +3
1
-1
2
-2
1
-1
2
-2
3
-3
Now let's see if it works by graphing
3x3+13x2 +13x +3
-1 so it works
An x-intercept is
Students who took this test also took :
Lesson simplifying radicals =
Lesson Naming Polynomials
Lesson: trig soh cah toa
Created with That Quiz — the site for test creation and grading in math and other subjects.