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2020 BC BLOCK ALGEBRA 2 > DECK 3: INTRO TO POLYNOMIAL TERMINOLOGY > Flashcards

DECK 3: INTRO TO POLYNOMIAL TERMINOLOGY Flashcards

1
Q

What is polynomial?

A

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

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2
Q

What is the DEGREE of a term?

A

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

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3
Q

What is the degree of this term?

5x

A

one

(because it can be written as 5x1)

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4
Q

What is the degree of this term?

3x4

A

four

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5
Q

What is the degree of this term?

7

A

zero

(It can be written as 7x0)

remember: anything raised to the zero power is 1

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6
Q

What is the degree of this term?

9x3

A

three

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7
Q

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

(with an exponent)

A

7x1

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8
Q

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

(with an exponent)

A

5x0

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9
Q

what is another way to write 6x0?

A

6

(because x0=1)

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10
Q

what is another way to write 9x1 ?

A

9x

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

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11
Q

What is the DEGREE of a polynomial?

A

The degree of the HIGHEST term.

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12
Q

What is the degree of this polynomial:

4-3x2-6x5 + 2x8

A

8

8 is the highest degreed term

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13
Q

What is the degree of this polynomial:

7x-1

A

one

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14
Q

What is the degree of this polynomial:

2x-2-3x+4x3

A

NOT A POLYNOMIAL

You can’t have negatives or fractions for exponents

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15
Q

A zero degree polynomial or term is called a _____.

example: 5

A

Constant

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16
Q

A first degree polynomial or term is called___

example: 3x

A

linear

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17
Q

A second degree polynomial is called _____

example: 5x2 -3x+ 6

A

quadratic

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18
Q

A third degree polynomial is called___

example: 6x3- 2x2- 8

A

cubic

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19
Q

A fourth degree polynomial or term is called _____

example: 3x4

A

quartic

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20
Q

A fifth degree polynomial is called _____

example: 3x5

A

quintic

(KWINTIC)

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21
Q

Does a cubic polynomial have thee terms?

A

Not necessarily. It has a highest exponent of three.

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

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22
Q

How do you know how many terms?

A

Count them

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23
Q

What is the “STANDARD” form of polynomials?

A

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

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24
Q

What degree is a cubic polynomial

A

third degree

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25
Q

Where does word “quadratics?” come from?

A

from latin “quadrus” which means SQUARE

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26
Q

Why is it called a “linear” term

A

alone its graph would be a straight line

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27
Q

why is it called a constant term

A

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

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28
Q

Why is it called the “quadratic” term?

A

because it is SQUARED… quadrus:square.

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29
Q

Why is it called the “cubic” term

A

because it is CUBED, to the third power

30
Q

12x5-2x3+4x2

What is the coefficient of the cubic term?

31
Q

56x5-3x3+4x2+8x

What is the coefficient of the linear term?

32
Q

6x5-3x3+4x2-2x

What is the quadratic term?

A

4x2

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

33
Q

2x5-3x3+4x2+6x-9

What is the coefficient of the constant term?

34
Q

3x5-3x3+4x2

What is the quintic term?

35
Q

QUADRATICS

What is the generic standard form of a quadratic?

You will see this a lot

A

y = ax2+bx+c

36
Q

QUADRATICS in standard form (ax2+bx+c)

f(x)= 3x2-4x+5

What is a, b and c ?

A

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

37
Q

QUADRATICS in standard form (ax2+bx+c)

f(x)= 5 - 2x +3x2

What is a, b and c ? (rearrange first)

(hint: ax2+bx+c)

A

a = 3

b = -2

c = 5

38
Q

QUADRATICS in standard form (ax2+bx+c)

f(x)= -4x2 + 8

What is a, b and c ?

A

a = -4,

b = 0,

c = 8

39
Q

QUADRATICS in standard form (ax2+bx+c)

f(x)= 3x - 9

What is a, b and c?

A

a = 0 , b = 3, c = 9..

There is no quadratic term..

THIS IS LINEAR!!!

IT’S A LINE!

slope of 3

40
Q

QUADRATICS in standard form (ax2+bx+c)

f(x)= 6x2- 7x

What is a, b and c ?

A

a = 6,

b=-7,

c = 0

41
Q

How do you know when it is a quadratic equation?

A

when the highest degreed term 2, the x2 term

(quadrus:square)

42
Q

How do you know when it is a linear equation?

A

When the highest degreed term is 1, the x term

(first degree)

43
Q

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

44
Q

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

45
Q

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

46
Q

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

47
Q

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

48
Q

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

A

only once. It is a line

49
Q

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

A

twice. The shape is a U, a parabola.

50
Q

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

A

Three times.

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

51
Q

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

A

Four times.

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

52
Q

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

A

Five times

53
Q

f(x)= 3x2-6x+3

What is the quadratic term?

54
Q

f(x)= 3x2-6x+3

What is the linear term?

55
Q

f(x)= 3x2-6x+3

What is the constant term?

A

3

it is the also the y intercept

56
Q

what is a coefficient?

A

the number in front of a variable or variables

57
Q

f(x)= 3x2-6x+3

What is the coefficient of the quadratic term?

A

3

this is also known as “a” for quadratics in standard form

58
Q

f(x)= 3x2-6x+3

What is the coefficient of the linear term?

A

-6

this is also known as “b” for quadratics in standard form

59
Q

f(x)= 3x2-6x+3

What is the coefficient of the constant term?

A

3

this is also known as “c” for quadratics in standard form

60
Q

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

61
Q

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

62
Q

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

63
Q

f(x) = ax2 + bx + c

What is the coefficient of the quadratic term?

64
Q

f(x) = ax2 + bx + c

What is the coefficient of the linear term?

65
Q

f(x) = ax2 + bx + c

What is the coefficient of the constant term?

A

c

(it is the y intercept)

66
Q

f(x) = ax2 + bx + c

What is the quadratic term?

A

ax2

It asked for the whole term, not just coefficient

67
Q

f(x) = ax2 + bx + c

What is the linear term?

68
Q

f(x) = ax2 + bx + c

What is the constant term?

A

c

(it is the y intercept)

69
Q

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

A

It is the constant term.

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

70
Q

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

A

y intercept

71
Q

WHAT MUST THE EXPONENTS BE IN A POLYNOMIAL?

A

POSITIVE WHOLE NUMBERS

2020 BC BLOCK ALGEBRA 2 (5 decks)

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