DECK 3: INTRO TO POLYNOMIAL TERMINOLOGY

Question 1

What is polynomial?

Answer 1

An expression with terms that have POSITIVE INTEGER exponents on the variables

Question 2

What is the DEGREE of a term?

Answer 2

The exponent (or sum of exponents if more than one variable).

Question 3

What is the degree of this term?

5x

Answer 3

one

(because it can be written as 5x¹)

Question 4

What is the degree of this term?

3x⁴

Answer 4

four

Question 5

What is the degree of this term?

7

Answer 5

zero

(It can be written as 7x⁰)

remember: anything raised to the zero power is 1

Question 6

What is the degree of this term?

9x³

Answer 6

three

Question 7

What is another way to write or to think of “7x?”

(with an exponent)

Answer 7

7x¹

Question 8

What is another way to write or to think of “5” to help you remember it has zero degrees?

(with an exponent)

Answer 8

5x⁰

Question 9

what is another way to write 6x⁰?

Answer 9

6

(because x⁰=1)

Question 10

what is another way to write 9x¹ ?

Answer 10

9x

(you generally don’t write and exponent of 1)

Question 11

What is the DEGREE of a polynomial?

Answer 11

The degree of the HIGHEST term.

Question 12

What is the degree of this polynomial:

4-3x²-6x⁵ + 2x⁸

Answer 12

8

8 is the highest degreed term

Question 13

What is the degree of this polynomial:

7x-1

Answer 13

one

Question 14

What is the degree of this polynomial:

2x^-2-3x+4x³

Answer 14

NOT A POLYNOMIAL

You can’t have negatives or fractions for exponents

Question 15

A zero degree polynomial or term is called a _____.

example: 5

Answer 15

Constant

Question 16

A first degree polynomial or term is called___

example: 3x

Answer 16

linear

Question 17

A second degree polynomial is called _____

example: 5x² -3x+ 6

Answer 17

quadratic

Question 18

A third degree polynomial is called___

example: 6x³- 2x²- 8

Answer 18

cubic

Question 19

A fourth degree polynomial or term is called _____

example: 3x⁴

Answer 19

quartic

Question 20

A fifth degree polynomial is called _____

example: 3x⁵

Answer 20

quintic

(KWINTIC)

Question 21

Does a cubic polynomial have thee terms?

Answer 21

Not necessarily. It has a highest exponent of three.

It can have one, two, or three + terms.

Question 22

How do you know how many terms?

Answer 22

Count them

Question 23

What is the “STANDARD” form of polynomials?

Answer 23

PUT THEM IN ORDER - List the terms (L to R) from highest degree to lowest degree

Question 24

What degree is a cubic polynomial

Answer 24

third degree

Question 25

Where does word "quadratics?" come from?

Answer 25

from latin "quadrus" which means SQUARE

Question 26

Why is it called a "linear" term

Answer 26

alone its graph would be a straight line

Question 27

why is it called a constant term

Answer 27

alone it would be a constant function.. The same height always. a horizontal line with a constant y, a constant height

Question 28

Why is it called the "quadratic" term?

Answer 28

because it is SQUARED... quadrus:square.

Question 29

Why is it called the "cubic" term

Answer 29

because it is CUBED, to the third power

Question 30

12x⁵-2x³+4x² What is the coefficient of the cubic term?

Answer 30

-2

Question 31

56x⁵-3x³+4x²+8x What is the coefficient of the linear term?

Answer 31

8

Question 32

6x⁵-3x³+4x²-2x What is the quadratic term?

Answer 32

4x² Notice that it asked for the entire term, not just the coefficient

Question 33

2x⁵-3x³+4x²+6x-9 What is the coefficient of the constant term?

Answer 33

-9

Question 34

3x⁵-3x³+4x² What is the quintic term?

Answer 34

3x⁵

Question 35

QUADRATICS What is the generic standard form of a quadratic? You will see this a lot

Answer 35

y = ax²+bx+c

Question 36

QUADRATICS in standard form (ax²+bx+c) f(x)= 3x²-4x+5 What is a, b and c ?

Answer 36

a = 3, b = -4, c = 5

Question 37

QUADRATICS in standard form (ax²+bx+c) f(x)= 5 - 2x +3x² What is a, b and c ? (rearrange first) (hint: ax²+bx+c)

Answer 37

a = 3 b = -2 c = 5

Question 38

QUADRATICS in standard form (ax²+bx+c) f(x)= -4x² + 8 What is a, b and c ?

Answer 38

a = -4, b = 0, c = 8

Question 39

QUADRATICS in standard form (ax²+bx+c) f(x)= 3x - 9 What is a, b and c?

Answer 39

a = 0 , b = 3, c = 9.. There is no quadratic term.. THIS IS LINEAR!!! IT'S A LINE! slope of 3

Question 40

QUADRATICS in standard form (ax²+bx+c) f(x)= 6x²- 7x What is a, b and c ?

Answer 40

a = 6, b=-7, c = 0

Question 41

How do you know when it is a quadratic equation?

Answer 41

when the highest degreed term 2, the x² term (quadrus:square)

Question 42

How do you know when it is a linear equation?

Answer 42

When the highest degreed term is 1, the x term (first degree)

Question 43

What is the maximum number of solutions for a linear equation?

Answer 43

1

Question 44

What is the maximum number of solutions for a quadratic equation?

Answer 44

2

Question 45

What is the maximum number of solutions for a cubic equation?

Answer 45

3

Question 46

What is the maximum number of solutions for a quartic equation?

Answer 46

4

Question 47

What is the maximum number of solutions for a quintic equation?

Answer 47

5

Question 48

What is the maximum number of times the graph of a linear function could cross the x axis? (max x-intercepts)

Answer 48

only once. It is a line

Question 49

What is the maximum number of times the graph of a quadratic function could cross the x axis? (max x-intercepts)

Answer 49

twice. The shape is a U, a parabola.

Question 50

What is the maximum number of times the graph of a cubic function could cross the x axis? (max x-intercepts)

Answer 50

Three times. The shape could be like a sideways S, up, down then up again.

Question 51

What is the maximum number of times the graph of a quartic function could cross the x axis? (max x-intercepts)

Answer 51

Four times. The shape could be like a W or upside down W.

Question 52

What is the maximum number of times the graph of a quintic function could cross the x axis?

Answer 52

Five times

Question 53

f(x)= 3x²-6x+3 What is the quadratic term?

Answer 53

3x²

Question 54

f(x)= 3x²-6x+3 What is the linear term?

Answer 54

-6x

Question 55

f(x)= 3x²-6x+3 What is the constant term?

Answer 55

3 it is the also the y intercept

Question 56

what is a coefficient?

Answer 56

the number in front of a variable or variables

Question 57

f(x)= 3x²-6x+3 What is the coefficient of the quadratic term?

Answer 57

3 this is also known as "a" for quadratics in standard form

Question 58

f(x)= 3x²-6x+3 What is the coefficient of the linear term?

Answer 58

-6 this is also known as "b" for quadratics in standard form

Question 59

f(x)= 3x²-6x+3 What is the coefficient of the constant term?

Answer 59

3 this is also known as "c" for quadratics in standard form

Question 60

what is the quadratic term's exponent on the x ?

Answer 60

2

Question 61

what is the linear term's exponent on the x ?

Answer 61

1

Question 62

what is the constant term's exponent on the x?

Answer 62

0

Question 63

f(x) = ax² + bx + c What is the coefficient of the quadratic term?

Answer 63

a

Question 64

f(x) = ax² + bx + c What is the coefficient of the linear term?

Answer 64

b

Question 65

f(x) = ax² + bx + c What is the coefficient of the constant term?

Answer 65

c (it is the y intercept)

Question 66

f(x) = ax² + bx + c What is the quadratic term?

Answer 66

ax² It asked for the whole term, not just coefficient

Question 67

f(x) = ax² + bx + c What is the linear term?

Answer 67

bx

Question 68

f(x) = ax² + bx + c What is the constant term?

Answer 68

c (it is the y intercept)

Question 69

For polynomials in standard form, how can you find the y intercept?

Answer 69

It is the constant term. If there is no constant term, then the y intercept is the origin (0,0)

Question 70

The constant term (the term without an x) will give you the _____ of the function.

Answer 70

y intercept

Question 71

WHAT MUST THE EXPONENTS BE IN A POLYNOMIAL?

Answer 71

POSITIVE WHOLE NUMBERS