Determine whether the statement is true or false. Justify your answer.If $(7 x+4)$ is a factor of some polynomial function $f$ then $rac{4}{7}$ is a zero of $f .$...

In Exercises 87 - 89, determine whether the statement is true or false. Justify your answer.

If $ (7x + 4) $ is a factor of some polynomial function $ f $, then $ \frac{4}{7} $ is a zero of $ f $.

Everyone today resolving problem number 98 in Chapter one section to the text book. This is a true false question, and you're asked to explain our reasoning. Um, so they give us this function right here. I love X peoples were experts one over seven X minus two in the state that it is a 10. It's a dental function and were asked to determine whether or not that something is true or false. So let's read these two particular sections that are about possible brain functions as either out Mental Chapter one, Section two. So we'll start the transcendent because that's what we keep balls was about. Uh thus far, we have discussed out great function, very function. Some functions, however, cannot be described a basic algebra operation. These functions are known as Transcendental Conference because they are turned set to transcend both want algebra. The most common types of transcendental functions are too much exponential on moderate bunch. It's okay, so I don't really see chicken. The lecture accidental along with our options here. And I do see Bates without a ride. So it's looking like this is going to be false. But before I make that decision. I'm going to be out of a function and see if the type of function I have been here is out by allowing for quotients are tract infection of powers and Paula, you know, intelligence. We need a larger possible option, and algae very function is one of them involves additions, attraction, multiplication division, rational powers and roots I. C. Division in mind. I was actually Division five. Two types of algebraic functions are national functions and fruit block ships. This says rational numbers are oceans of integers. National functions are oceans apart. Well, I actually have a rational function right here. This isn't rational function because I have the quotient of this. Probably know mia on that, and it follows this form, right? Pee vacs over. Q. That's it looks very similar to this what you want. So because this is because after that is irrational function, it is algebra, So this is false. It's not funny, transcendental. It's gonna be algebraic. And again, I fits the textbook definition of an algebraic function, cause it says two types of outbreak functions are rational functions and boot functions. So we have a division two polling numbers, which makes this rational. All right, rational functions are ultra great. So in general, if you're going to say false, tow any statement about if it is a transit much function, you have to explain why it's another classification of a function in this particular who's this is out straight. So there you have it. If you guys enjoying my explanation of this problem using like, but that's it state and thank you for watching.

This statement is actually going to be false. And here's why we mentioned that there is a factor of X plus two. But keep in mind when the factors X plus two, that means K equals negative two. So what that really means is that, um, f of negative two is going to equal zero, not f of two. So half of two will not necessarily equal zero. Um, so that is why this statement is false.

Open number 47. Ah, there is exactly a hyper pulling function such that a belongs all the equation of threats has a me total one. It's a went through shine Thanks. And they're graph is equal to which found it too. We're this is a and efficiency.

So the statement you see is that if effigy final nipples have to get on immune function off before Okay, all degree four and f off to the value off off to 30 was too fine. OK, then we have a four x upon X minus two ID equals do he off eggs? You have your ex bless off 51 what we say five divided by X minus two. Then you need to check that this given statement is true. Ofcourse there. B x is a one year from some off duty three. Okay, So let me tell you guys that this is up, that district mint is true. And let me tell you how because we all know that very degree. Ample. Noon on the degree on D V at four. Fax is divided by degree one polynomial x minus C. Then the result is a bigly and minus one point union broken. Your fix your ex less arnold things upon X minus. See, there are six Model X. He was to a bowel. See? Okay, then this is the statement for division algorithm for polynomial right away that this is the statement deism. I didn't Oh, are also didn't algorithm. Well, for the No, you're okay. So this whole statement was completely that is an album statement and that statement with