5.5-5.7 Flashcards Preview

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Flashcards in 5.5-5.7 Deck (18):
1

End behavior for leading coefficient positive and degree sign even

Open up quadratic

2

End behavior for leading coefficient negative and degree sign even

Open down quadratic

3

End behavior for leading coefficient positive and degree sign odd

Positive linear line

4

End behavior for leading coefficient negative and degree sign odd

Negative linear line

5

Use long division

Just like division
Put remainder over what divided by

6

Remainder theorem

If polynomial y is divided by x-k, then the remainder is y

7

Remainder theorem example

Used in synthetic division, what's the last number is the remainder

8

Synthetic division

Divide by x+2, so x=-2, put in box, use synthetics, then what you get add x's and the last number is the remainder
Ex 1,2,-9, 21
1x cubed+ 2x squared-9+ 21/x+2

9

Factor theorem

Y has factor x-k if and only if y=o

10

Factor polynomial given
x-k

Do synthetic division, then do (x-k)(what was left from division) then factor

11

Find other zeros when given a zero

Use that zero to plug into for synthetic division in the box, then factor

12

Rational zero theorem

If polynomial has integers as coefficients then every rational zero has this form
P/Q= factor of constant over factor of leading coeifficent

13

Apply rational zero theorem

LC:1
C:2,4,6
So possibles are 2/1,4/1,6/1 all plus or minus

14

Find all real zeros using calc

2nd
Y=
Graph

15

Find all zeros

Synthetic division after guessing with LC and C

16

Complex conjugate and irrational

If one is present both are, so plus or minus
Ex a-bi so there is a-bi AND a+bi

17

(A+b)(a-b)

A^2-B^2

18

Descartes rule of signs

Positive real zeros is equal to number of changed signs and this minus even
Negative is change of sign of f(-x) and this less than odd number