Factoring Polynomials and Solving Flashcards Preview

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Flashcards in Factoring Polynomials and Solving Deck (74)
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1

When factoring by grouping, what is the first step?

Split the expression into two parts.

2

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

Match

3

What are the matching parts considered to be?

The GCF

4

If the first term is positive what is the GCF?

The GCF is positive.

5

If the first term is negative what is the GCF?

The GCF is negative.

6

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

1. Look for an error.
2. It cannot factor.

7

What is used to check the factored expressions?

FOIL

8

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

Difference of perfect squares

9

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

Crummy crummy SOPS

10

Crummy crummy SOPS: crummy crummy =

cube root, cube root

11

Crummy crummy SOPS: S =

square

12

Crummy crummy SOPS: OP =

opposite product

13

Crummy crummy SOPS: second S =

square

14

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)

Factoring a sum or difference of cubes

15

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

The biggest exponents.

16

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

Nothing, don't worry.

17

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

FOIL
and make sure to look for a difference of squares.

18

Check for ____ _____ before circling final answer.

Cube roots

19

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

Graph or quadratic formula.

20

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

real solutions

21

If there are no real solutions, there are

imaginary solutions

22

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

quadratic formula.

23

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

Monomial

24

Polynomial vocabulary: the exponent.

Degree of a monomial

25

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

Polynomial

26

Polynomial vocabulary: the greatest exponent.

Degree of a polynomial

27

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

Standard form of a polynomial

28

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

Binomial

29

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

Trinomial

30

Polynomial vocabulary: the number before a variable.

Coefficient