DECK 3 - FACTOR - ROOT - REMAINDER

Question 1

Other names for zeros?

Answer 1

roots, zeros, solutions, x-intercepts.

Question 2

Other names for roots?

Answer 2

roots, zeros, solutions, x-intercepts.

Question 3

Other names for x-intercepts?

Answer 3

roots, zeros, solutions, x-intercepts.

Question 4

Other names for solutions?

Answer 4

roots, zeros, solutions, x-intercepts.

Question 5

A linear equation has ___ roots

Answer 5

1

Question 6

A quadratic equation has ___ roots

Answer 6

2

Question 7

A cubic equation has ____ roots

Answer 7

3

Question 8

A quartic equation has ____ roots

Answer 8

4

Question 9

A quintic equation has ___ roots

Answer 9

5

Question 10

An 10th degree equation has ___ roots

Answer 10

10

Question 11

An nth degee equation has ___ roots

Answer 11

n

Question 12

f(x)=(x-5)(x-5)(x+3)(x+3)
What degree?
How many roots?
How many UNIQUE roots? (what are they?)

Answer 12

Fourth Degree (QUARTIC)
FOUR ROOTS: 5, 5, -3, -3
TWO UNIQUE ROOTS: 5 and -3

Question 13

What is the fundamental theorem of algebra?

Answer 13

“An “Nth” degree equation has N roots.

Question 14

What theorem tells us that an N’th degree equation has N roots?

Answer 14

THE
FUNDEMENTAL
THEOREM OF
ALGEBRA

Question 15

12/3=4 what is divisor?

Answer 15

3

Question 16

12/3=4 what is dividend?

Answer 16

12

Question 17

12/3=4 what is quotient?

Answer 17

4

Question 18

If (x-5) is a factor, then ____ is a root.

Answer 18

5

Question 19

If (x+2) is a factor, then ____ is a zero.

Answer 19

-2

Question 20

If (x-M) is a factor, then ____ is an x -intercept.

Answer 20

M

Question 21

If (x-5) is a factor, then ____ is a y -intercept.

Answer 21

YOU CAN’T TELL WHAT THE Y INTERCEPT IS. Factors only tell you about x-intercepts

Question 22

(x-0) is the same as x.
If x is a factor, then ____ is a root.

Answer 22

0

Question 23

if x is a factor then _____ is an x intercept

Answer 23

0

Question 24

If -6 is a zero, then _____ is a factor

Answer 24

(x+6)

Question 25

If 0 is a root then ___ is a factor

Answer 25

(x-0) or JUST x

Question 26

If 2 is an x-intercept then ____ is a factor

Answer 26

(x-2)

Question 27

if 0 is an x intercept, then ___ is a factor

Answer 27

x
which is the same as x-0

Question 28

If -45 is a root then ____ is a factor

Answer 28

(x + 45)

Question 29

If (2x-5) is a factor, how do you find the zero?

Answer 29

Set 2x-5=0 and solve for x (two steps)
2x = 5
x = 5/2

Question 30

If (10x+7) is a factor, how do you find the zero?

Answer 30

Set 10x+7=0 and solve for x (two-steps)
10x = -7
x= -7/10

Question 31

If the graph passes through (8,0), which is 8 on the x axis, then you know that ____ is a factor.

Answer 31

(x-8)

Question 32

If x is a factor, then you know that the graph passes through ______

Answer 32

the origin, (0,0)

Question 33

If a graph passes through -5 on the x axis, what do you know is a factor?

Answer 33

(x+5) is a factor

Question 34

If 3x is a factor then you know the graph passes through

Answer 34

The origin
3x=0 when x=0

Question 35

If p is a root then ___ is a factor

Answer 35

(x-p) is a factor

Question 36

If a function goes through the origin, (0,0), then you know that ____ is a factor

Answer 36

x

Question 37

If -m is a zero then ____ is a factor

Answer 37

(x+m)

Question 38

If you divide a polynomial by (x-5), how do know if it is a factor?

Answer 38

If the remainder is zero

Question 39

If you divide a polynomial by (x+30), how do know if -30 is a root?

Answer 39

If the remainder is zero

Question 40

If you divide a polynomial by (x-5), and get a remainder of zero, What two things do you know?

Answer 40

You know (x-5) is a factor and that 5 is a root

Question 41

If you divide a polynomial by (x+9), and get a remainder of 15, What two things do you know?

Answer 41

You know that (x+9) is NOT a factor and that -9 is NOT a root

Question 42

If you want to find out if 7 is a root of a polynomial, what can you do?

Answer 42

divide it by (x-7) and if the remainder is 0, then 7 is a root.

Question 43

If you want to find out if -8 is a root of a polynomial, what can you do?

Answer 43

divide it by (x+8) and if the remainder is 0, then -8 is a root.

Question 44

If you want to find out if (x-12) is a factor of a polynomial, what can you do?

Answer 44

divide by (x-12) and if the remainder is zero, then 12 is a root.

Question 45

If you get a remainder of zero what do you know?

Answer 45

that the divisor is a factor.

Question 46

If you get a remainder of -3 what do you know?

Answer 46

that the divisor is NOT a factor.

Question 47

In synthetic division, what goes in the little box in top left?

Answer 47

The ROOT
the ZERO
(not the factor)

Question 48

If you are doing synthetic division, and are dividing by (x-8), what do you put in the box?

Answer 48

8

Question 49

If you are doing synthetic division, and are dividing by (x+12), what do you put in the box?

Answer 49

-12

Question 50

If you want to see if 8 is a root with synthetic division, what do you put in the box?

Answer 50

8

Question 51

HOW CAN YOU FIND THE Y INTERCEPT FOR ANY FUNCTION?

Answer 51

Set all the x=0 and solve for y

Question 52

What do you have to watch out for with the exponents in synthetic and long division?
2 THINGS

Answer 52

1. They are in descending order
   2 They are all there (put 0 in for missing terms)

Question 53

If you want to see if -9 is a root with synthetic division, what do you put in the box?

Answer 53

-9