DECK 3 - FACTOR - ROOT - REMAINDER Flashcards
Other names for zeros?
roots, zeros, solutions, x-intercepts.
Other names for roots?
roots, zeros, solutions, x-intercepts.
Other names for x-intercepts?
roots, zeros, solutions, x-intercepts.
Other names for solutions?
roots, zeros, solutions, x-intercepts.
A linear equation has ___ roots
1
A quadratic equation has ___ roots
2
A cubic equation has ____ roots
3
A quartic equation has ____ roots
4
A quintic equation has ___ roots
5
An 10th degree equation has ___ roots
10
An nth degee equation has ___ roots
n
f(x)=(x-5)(x-5)(x+3)(x+3)
What degree?
How many roots?
How many UNIQUE roots? (what are they?)
Fourth Degree (QUARTIC)
FOUR ROOTS: 5, 5, -3, -3
TWO UNIQUE ROOTS: 5 and -3
What is the fundamental theorem of algebra?
“An “Nth” degree equation has N roots.
What theorem tells us that an N’th degree equation has N roots?
THE
FUNDEMENTAL
THEOREM OF
ALGEBRA
12/3=4 what is divisor?
3
12/3=4 what is dividend?
12
12/3=4 what is quotient?
4
If (x-5) is a factor, then ____ is a root.
5
If (x+2) is a factor, then ____ is a zero.
-2
If (x-M) is a factor, then ____ is an x -intercept.
M
If (x-5) is a factor, then ____ is a y -intercept.
YOU CAN’T TELL WHAT THE Y INTERCEPT IS. Factors only tell you about x-intercepts
(x-0) is the same as x.
If x is a factor, then ____ is a root.
0
if x is a factor then _____ is an x intercept
0
If -6 is a zero, then _____ is a factor
(x+6)
If 0 is a root then ___ is a factor
(x-0) or JUST x
If 2 is an x-intercept then ____ is a factor
(x-2)
if 0 is an x intercept, then ___ is a factor
x
which is the same as x-0
If -45 is a root then ____ is a factor
(x + 45)
If (2x-5) is a factor, how do you find the zero?
Set 2x-5=0 and solve for x (two steps)
2x = 5
x = 5/2
If (10x+7) is a factor, how do you find the zero?
Set 10x+7=0 and solve for x (two-steps)
10x = -7
x= -7/10
If the graph passes through (8,0), which is 8 on the x axis, then you know that ____ is a factor.
(x-8)
If x is a factor, then you know that the graph passes through ______
the origin, (0,0)
If a graph passes through -5 on the x axis, what do you know is a factor?
(x+5) is a factor
If 3x is a factor then you know the graph passes through
The origin
3x=0 when x=0
If p is a root then ___ is a factor
(x-p) is a factor
If a function goes through the origin, (0,0), then you know that ____ is a factor
x
If -m is a zero then ____ is a factor
(x+m)
If you divide a polynomial by (x-5), how do know if it is a factor?
If the remainder is zero
If you divide a polynomial by (x+30), how do know if -30 is a root?
If the remainder is zero
If you divide a polynomial by (x-5), and get a remainder of zero, What two things do you know?
You know (x-5) is a factor and that 5 is a root
If you divide a polynomial by (x+9), and get a remainder of 15, What two things do you know?
You know that (x+9) is NOT a factor and that -9 is NOT a root
If you want to find out if 7 is a root of a polynomial, what can you do?
divide it by (x-7) and if the remainder is 0, then 7 is a root.
If you want to find out if -8 is a root of a polynomial, what can you do?
divide it by (x+8) and if the remainder is 0, then -8 is a root.
If you want to find out if (x-12) is a factor of a polynomial, what can you do?
divide by (x-12) and if the remainder is zero, then 12 is a root.
If you get a remainder of zero what do you know?
that the divisor is a factor.
If you get a remainder of -3 what do you know?
that the divisor is NOT a factor.
In synthetic division, what goes in the little box in top left?
The ROOT
the ZERO
(not the factor)
If you are doing synthetic division, and are dividing by (x-8), what do you put in the box?
8
If you are doing synthetic division, and are dividing by (x+12), what do you put in the box?
-12
If you want to see if 8 is a root with synthetic division, what do you put in the box?
8
HOW CAN YOU FIND THE Y INTERCEPT FOR ANY FUNCTION?
Set all the x=0 and solve for y
What do you have to watch out for with the exponents in synthetic and long division?
2 THINGS
- They are in descending order
2 They are all there (put 0 in for missing terms)
If you want to see if -9 is a root with synthetic division, what do you put in the box?
-9
