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Know the effect of factors of the form (x-a)2 and (x-a)3 has on the graph of a polynomial

thats the question i have to answer O.o

I already know some about polynomials and things and I've gone through textbooks, internet sites and now I'm going to a forum because I don't seem to be able to find anything to help me. Any help is great :D thanks guys

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Know the effect of factors of the form (x-a)2 and (x-a)3 has on the graph of a polynomial

thats the question i have to answer O.o

I already know some about polynomials and things and I've gone through textbooks, internet sites and now I'm going to a forum because I don't seem to be able to find anything to help me. Any help is great :D thanks guys

A factor means that it is part of some larger product.

Say that the polynomial is

P(x) = (x-a)^2 * f(x)

where f(x) is some other polynomial.

What happens if x=a?

What is the value of the function here?

What is the slope here?

Now try P(x) = (x-a)^3 * f(x)

What happens if x=a?

What is the value of the function here?

What is the slope here?

How is the slope changing here?

Try doing this for different values for a and for simple polynomials for f(x) like

f(x) = (x-5) where a is not equal to 5

or

f(x) = 1

or

...

Edited by mmiguel1
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