Question

What is the remainder when (x3 − 6x2 − 42x + 79) is divided by (x + 5)?

Answer 1

use reminder theorem
The remainder when P(x) is divided by (x - a) = f(a)

Answer 2

so here you need to find P(-5)

Answer 3

i tried plugging in -5, but i kept getting numbers that weren't in the answer choices

Answer 4

(P(x) is your polynomial)

Answer 5

oh maybe the choices are all wrong
i'll see what i get

Answer 6

okay thank you

Answer 7

i get 14

Answer 8

f(-5) = -125 - 150 - (42*-5) + 79

Answer 9

thats one of the answer choices! and i was doing +150 idk why lol oops

Answer 10

can you help me with one more

Answer 11

ok

Answer 12

Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the end behavior.

Answer 13

well the y-intercept occurs when x = 0
so find f(0) and you get that one

Answer 14

okay, is the end behavior down?

Answer 15

hold on

Answer 16

and i got -36 for the y-intercept

Answer 17

right

Answer 18

yay

Answer 19

its been a while since i did end behaviours
fo find the x intercepts we need to solve
x^3 -11x^2 + 36x - 36

Answer 20

So set it equal to 0?

Answer 21

yes

Answer 22

as the last number is 36 we could try 2,3 and 6 to see if they are roots

Answer 23

Can there be more than one answer when you do that tho

Answer 24

f(2) = 8 - 44 + 72 - 36 = 0

yes x=2 is one x-intercept

Answer 25

i think they all work

Answer 26

yes they do
thats is pure luck!!!!

Answer 27

lol

Answer 28

I think the end behavior is down because it hits x at 3 points

Answer 29

normally i would divide the polynomial by x - 2 and try to factor the quotient

Answer 30

no i dont think we can say that
as the last zero is 6 try finding f(7) and f(8) and see if they are increasing or decreasing

Answer 31

f(7) = 20 f(8) = 60

so end behaivour is increasing

Answer 32

so up? lol

Answer 33

yes

Answer 34

yay! thank you so much!

Answer 35

i'll draw the graph on my calculator to confirm

Answer 36

yep it looks somthing like