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do you know how to find when the polynomial f is zero?
here is a hint if you have a*b=0 then a=0 or b=0 or both=0 so you solve x-4=0 and (x-1)^4=0 also you can determine the multiplicity of the zero by looking at the power
So you just plug 0 in where x is?
you plug in 0 where y is or where f(x) is..
But there is no Y in the equation?
y=f(x) this is why I said or where f(x) is
To find the x-intercepts you set y to 0 To find the y-intercept you set x to 0 --- f(x)=y
\[y=3(x-4)(x-1)^4 \\ 0=3(x-4)(x-1)^4\]
so you then solve for x?
yes if you want to find the x-intercepts
I'm still confused on how to fine the answer for what I want to find???
did you read what I first said.. "here is a hint if you have a*b=0 then a=0 or b=0 or both=0 so you solve x-4=0 and (x-1)^4=0 also you can determine the multiplicity of the zero by looking at the power "
Yes, I read that...but (AGAIN) I am still confused...I don't understand what you mean??
so you are unable to solve x-4=0? and also unable to solve (x-1)^4=0?
the first one would be x=4 I don't know how to do the second one...
do you know 0^4 is 0?
or you can think it like this (x-1)^4=0 is equivalent to (x-1)(x-1)(x-1)(x-1)=0
and again using that if you have a*b=0 then a=0 or b=0 or both=0
you have x-1=0 or x-1=0 or x-1=0 or x-1=0
can you solve x-1=0?
right and you have that equation 4 times because of that power of 4 which tells you have x=1 multiplicity 4
ok, so does it touch or cross the x-axis?
you can look at a graph but zeros associated with even multiplicities means you will have a touch and zeros associated with odd multiplicities means you will have a cross