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Algebra 2 > Factoring Polynomials and Solving > Flashcards

Factoring Polynomials and Solving Flashcards

1
Q

When factoring by grouping, what is the first step?

A

Split the expression into two parts.

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2
Q

Step two: what do the two parenthesis need to do in order to continue factoring?

A

Match

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3
Q

What are the matching parts considered to be?

A

The GCF

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4
Q

If the first term is positive what is the GCF?

A

The GCF is positive.

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5
Q

If the first term is negative what is the GCF?

A

The GCF is negative.

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6
Q

Step two: if the two parentheses don’t match what two things can you do?

A
  1. Look for an error.

2. It cannot factor.

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7
Q

What is used to check the factored expressions?

A

FOIL

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8
Q

To be sure that you are done factoring, what do you look for?

A

Difference of perfect squares

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9
Q

When factoring a sum or a difference of cubes, what is the phrase to remember?

A

Crummy crummy SOPS

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10
Q

Crummy crummy SOPS: crummy crummy =

A

cube root, cube root

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11
Q

Crummy crummy SOPS: S =

A

square

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12
Q

Crummy crummy SOPS: OP =

A

opposite product

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13
Q

Crummy crummy SOPS: second S =

A

square

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14
Q

What is this formula used for:
a^3 + b^3 = (a+b) (a^2 - ab + b^2)
OR
a^3 - b^3 = (a-b) (a^2 + ab + b^2)

A

Factoring a sum or difference of cubes

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15
Q

When solving polynomial equations, what tells how many solutions there are?

A

The biggest exponents.

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16
Q

When factoring in quadratic form, what do you do if the exponents are twice as much (for example ax^4 + bx^2 + c)

A

Nothing, don’t worry.

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17
Q

How do you check to see if you are done factoring?

A

FOIL

and make sure to look for a difference of squares.

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18
Q

Check for ____ _____ before circling final answer.

A

Cube roots

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19
Q

If an equation cannot factor or square root, what are the two other options for solving?

A

Graph or quadratic formula.

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20
Q

If it doesn’t hit the x-axis it doesn’t have any ____ _________.

A

real solutions

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21
Q

If there are no real solutions, there are

A

imaginary solutions

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22
Q

Because you can’t graph points that don’t hit the x-axis, to solve a problem with imaginary solutions use

A

quadratic formula.

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23
Q

Polynomial vocabulary: one term; a number or a variable.

A

Monomial

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24
Q

Polynomial vocabulary: the exponent.

A

Degree of a monomial

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25
Q

Polynomial vocabulary: one or more terms connected by plus or minus.

A

Polynomial

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26
Q

Polynomial vocabulary: the greatest exponent.

A

Degree of a polynomial

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27
Q

Polynomial vocabulary: In order with the largest exponent first, then descending.

A

Standard form of a polynomial

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28
Q

Polynomial vocabulary: used to describe and classify polynomials with two terms.

A

Binomial

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29
Q

Polynomial vocabulary: used to describe and classify polynomials with three terms.

A

Trinomial

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30
Q

Polynomial vocabulary: the number before a variable.

A

Coefficient

31
Q

Polynomial vocabulary: first coefficient in standard order.

A

Leading coefficient

32
Q

Polynomial vocabulary: the term that doesn’t change with the variable; doesn’t have a variable; always comes last in standard order.

A

Constant

33
Q

Classifications: degree 0

A

Constant

34
Q

Classifications: degree 1

A

Linear

35
Q

Classifications: degree 2

A

Quadratic

36
Q

Classifications: degree 3

A

Cubic

37
Q

Classifications: degree 4

A

Quartic

38
Q

Classifications: degree 5

A

Quintic

39
Q

Polynomial vocabulary: describes where the graph is going; how the arrows point.

A

End behavior

40
Q

Polynomial vocabulary: where the graph changes direction.

A

Turning points

41
Q

Hint: the number of turning points is ___ ____ than the degree of the function.

A

one less

42
Q

If
Degree: odd
LC: positive
what is the end behavior?

A

L: falls
R: rises

43
Q

If
Degree: odd
LC: negative
what is the end behavior?

A

L: rises
R: falls

44
Q

If
Degree: even
LC: positive
what is the end behavior?

A

L: rises
R: rises

45
Q

If
Degree: even
LC: negative
what is the end behavior?

A

L: falls
R: falls

46
Q

Given a #z and a polynomial (P) in standard form, x - z is a factor of the polynomial

A

If one is true then they all are.

47
Q

Given a #z and a polynomial (P) in standard form, z is a zero of the polynomial function

A

If one is true then they all are.

48
Q

Given a #z and a polynomial (P) in standard form, z is a root/solution of the polynomial equation P(x)=0

A

If one is true then they all are.

49
Q

Given a #z and a polynomial (P) in standard form, z is an x-intercept of the graph y=P(x)

A

If one is true then they all are.

50
Q

If there is no number before a factor, then

A

The leading coefficient is zero.

51
Q

To find the y-intercept from the zeros,

A

use x=0

52
Q

If it doesn’t factor,

A

plug it into the calculator.

53
Q

What tools on the calculator do you use to find the relative minimum/maximum

A

CALC

54
Q

How many relative minimums/maximum can you have?

A

There is no limit to how many you can have.

55
Q

To divide two polynomials, use

A

Polynomial long division

56
Q

What is the answer to a division problem called?

A

Quotient

57
Q

What is the number being divided called?

A

Dividend

58
Q

What is the number on the outside of the long division symbol called?

A

Divisor

59
Q

What is the number left over after division called?

A

Remainder

60
Q

What is another name for synthetic division?

A

Fake division

61
Q

Synthetic division steps: 1

A

Standard form and every lower exponent must be there.

62
Q

Synthetic division steps: 2

A

Coefficients go down below the upside-down division symbol.

63
Q

Synthetic division steps: 3

A

Add the free zero.

64
Q

Synthetic division steps: 4

A

Think: add then multiply

65
Q

For synthetic long division, if the problem starts with x^4 the answer will start with

A

x^3

66
Q

Synthetic long division can only be used for problems with

A

x + #
and
x - #

67
Q

Name this process: You list the standard-form coefficients (including zeros) of the polynomial, omitting all variables and exponents. You use “a” for the divisor and add instead of subtract throughout the process.

A

Synthetic division

68
Q

What is it if you divide a polynomial P(x) by x-a, then the remainder = P(a)?

A

Remainder theorem

69
Q

What can you sometimes use to check a factor and/or help you factor?

A

Division

70
Q

From factoring by grouping, if the two terms in parentheses don’t match, what can you do?

A

Use synthetic division (sneaky factoring).

71
Q

After using “sneaky factoring” (synthetic division), what do you do if the problem isn’t factored all the way?

A

Use the box method to factor further.

72
Q

How do you find the y-intercept from the x’s?

A

Plug in zero for x and multiply what is left together.

73
Q

When figuring out which regression to use (linear, quadratic, cubic, quartic, etc.), what do you look for?

A

The R^2 value to be closest to 1.

74
Q

What numbers will always have it’s opposite as a factor?

A

Radical and imaginary roots.

Algebra 2 (9 decks)

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