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

- anonymous

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

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- welshfella

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

- welshfella

so here you need to find P(-5)

- anonymous

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

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## More answers

- welshfella

(P(x) is your polynomial)

- welshfella

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

- anonymous

okay thank you

- welshfella

i get 14

- welshfella

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

- anonymous

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

- anonymous

can you help me with one more

- welshfella

ok

- anonymous

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

- welshfella

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

- anonymous

okay, is the end behavior down?

- welshfella

hold on

- anonymous

and i got -36 for the y-intercept

- welshfella

right

- anonymous

yay

- welshfella

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

- anonymous

So set it equal to 0?

- welshfella

yes

- welshfella

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

- anonymous

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

- welshfella

f(2) = 8 - 44 + 72 - 36 = 0
yes x=2 is one x-intercept

- anonymous

i think they all work

- welshfella

yes they do
thats is pure luck!!!!

- welshfella

lol

- anonymous

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

- welshfella

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

- welshfella

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

- welshfella

f(7) = 20 f(8) = 60
so end behaivour is increasing

- anonymous

so up? lol

- welshfella

yes

- anonymous

yay! thank you so much!

- welshfella

i'll draw the graph on my calculator to confirm

- welshfella

yep it looks somthing like
|dw:1438439995445:dw|

- anonymous

yayy

- welshfella

yea its always worth doing a check on factors of the last number especially if its a composite number like 36

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