Mth 158
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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I am having such a hard time understanding section 5.5. I have been reading and trying to figure out how to do it, but I just can't seem to do it.
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For Descartes' Rule of Signs.
I can see that the highest degree would determine the maximum number of real zeros. I understand the number of variations in the sign of the nonzero coefficients of f(x).
But, for example: f(x) = 3x^6 - 4x^4 + 3x^3 + 2x^2 - x - 3
I see that there are 3 variations in the signs. Then if you look at f(-x)
f(-x) = 3(-x)^6 - 4(-x)^4 + 3(-x)^3 + 2(-x)^2 - (-x) -3 = 3x^6 - 4x^4 - 3x^3 + 2x^2 + x - 3
Up until this point it is clear. Then it says there are three var5iations in sign, so we expectt either three or one negative real zero. (What does that mean, and how did they come to that conclusion?) Then it has either three or one positive x-intercepts and three or one negative x-intercepts. (Again, how do they get this?)
Without knowing for certain the above question, I can't get past Finding the Rational Zeros of a Polynomial Function. Some of the steps include:
Step 1: The most real zeros (which would be the largest of the degree)
Step 2: Descartes' Rule of Signs (not yet understood)
Step 3: List of potential rational zeros (I am thinking it the factors of the constant and the leading coefficient of the highest degree) So, for example, f(x) = 2x^3 + 11x^2 - 7x - 6 would be
positive or negative 1 * 6 or 2 * 3 and positive or negative 1 * 2......is this correct?
Then testing you would do the following:
f(1) f(6) f(2) f(3) into the equation to see if it equals 0?
Step 4: The depressed equation I think I understand if I can just get the above steps.
I had a question the other day about long division of polynomials. Today after studying ch 5.3 I remember now that you can use synthetic division (which I understand completely) is this true for all division of polynomials or just in this instance for ch 5.3?
Section 5.5 is not assigned.
You should move on to Chapter 6.
If you still want to explore these questions after completing the required sections of the text, I'll be glad to answer them. Just resubmit the document at that time. However this is not required either in this course or in precalculus.