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use reminder theorem The remainder when P(x) is divided by (x - a) = f(a)
so here you need to find P(-5)
i tried plugging in -5, but i kept getting numbers that weren't in the answer choices
(P(x) is your polynomial)
oh maybe the choices are all wrong i'll see what i get
okay thank you
i get 14
f(-5) = -125 - 150 - (42*-5) + 79
thats one of the answer choices! and i was doing +150 idk why lol oops
can you help me with one more
Describe the graph of the function f(x) = x3 − 11x2 + 36x − 36. Include the y-intercept, x-intercepts, and the end behavior.
well the y-intercept occurs when x = 0 so find f(0) and you get that one
okay, is the end behavior down?
and i got -36 for the y-intercept
its been a while since i did end behaviours fo find the x intercepts we need to solve x^3 -11x^2 + 36x - 36
So set it equal to 0?
as the last number is 36 we could try 2,3 and 6 to see if they are roots
Can there be more than one answer when you do that tho
f(2) = 8 - 44 + 72 - 36 = 0 yes x=2 is one x-intercept
i think they all work
yes they do thats is pure luck!!!!
I think the end behavior is down because it hits x at 3 points
normally i would divide the polynomial by x - 2 and try to factor the quotient
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
f(7) = 20 f(8) = 60 so end behaivour is increasing
so up? lol
yay! thank you so much!
i'll draw the graph on my calculator to confirm
yep it looks somthing like |dw:1438439995445:dw|
yea its always worth doing a check on factors of the last number especially if its a composite number like 36