At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Here's an idea: ask *how* to do it, not what the answer is.
I'm not asking for the answer. I would like to know how to solve the problems.
To both of you, I was thinking about the same thing! @Anickyan , to be precise, nothing was asked yet... @Amarie31 , similarly, you did not ask anything. Normally people will see a problem and maybe walk you through it. I think the best way to learn, when there isn't a community to help, is to formulate specific questions, like, "what is the degree of a polynomial?" Or others. Sometimes you have to delve into the problem just to find what to ask, and you learn how to do it in the process! That's great! And for interactive help, OpenStudy is here :) So, where are you having a problem? If you're like I am/was, you'll look at it and say "the whole thing." But now I more usually try to make sure I understand the question thoroughly - every word - before I decide I don't know what to do. Do you have a specific problem, or do you want a hint?
I only have one half hour to help right now!
I don't understand problem 53
So, maybe I can help you understand everything. Do you know what the degree of a polynomial is?
No I do not know
Okay! Well, you find the term where the variable(s) have the highest powers combined. I assume you're just using one variable, so the "order" is the same number as the highest power. Well, a polynomial has many terms (added/subtracted pieces) and the varibles have different exponents, like \(2x^2+x+4\). So, the \(2x^2\) has the highest power, \(2\). So the order is \(2\), so second order.
Alright that makes sense
Now, these polynomials can make funky curves, like |dw:1377538217745:dw|and stuff like that.
You want to know what order the polynomial CANNOT BE to have just three points on the axis. The maximum number of times a function can cross the \(x\)-axis depends somewhat on the order. If you have a first order, it is like \(ax^1\pm b\). That is a line, and will cross once. If you have a second order, it is like \(ax^2\pm bx\pm c\). That could cross twice. 3 could cross three times, 4 could cross four, and so on. Okay?
Yes I understand
Okay! So, your polynomial crosses 3 times. Could maybe have more bumps, but crosses just 3. So the polynomial must have at least what order to make at least 3 crosses?
Right. So, if you order is \(n\), and the order must be 3 or more, so \(n\ge 3\), what cannot be true?
Right! I have to go. Take care!
Thanks so much
Now, notice how we broke down the problem. You might not have known that the max number of crosses is the order, but now you do! :)
You helped a lot!