5.5-5.7 Flashcards
End behavior for leading coefficient positive and degree sign even
Open up quadratic
End behavior for leading coefficient negative and degree sign even
Open down quadratic
End behavior for leading coefficient positive and degree sign odd
Positive linear line
End behavior for leading coefficient negative and degree sign odd
Negative linear line
Use long division
Just like division
Put remainder over what divided by
Remainder theorem
If polynomial y is divided by x-k, then the remainder is y
Remainder theorem example
Used in synthetic division, what’s the last number is the remainder
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
Factor theorem
Y has factor x-k if and only if y=o
Factor polynomial given
x-k
Do synthetic division, then do (x-k)(what was left from division) then factor
Find other zeros when given a zero
Use that zero to plug into for synthetic division in the box, then factor
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
Apply rational zero theorem
LC:1
C:2,4,6
So possibles are 2/1,4/1,6/1 all plus or minus
Find all real zeros using calc
2nd
Y=
Graph
Find all zeros
Synthetic division after guessing with LC and C
