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Use the Rational Zero Theorem to list all possible rational zeros for each given function.$$f(x)=x^{3}+x^{2}-4 x-4$$...

Question

Use the Rational Zero Theorem to list all possible rational zeros for each given function.$$f(x)=x^{3}+x^{2}-4 x-4$$

Use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=x^{3}+x^{2}-4 x-4 $$



Answers

List all possible rational zeros for the functions.
$$f(x)=x^{4}+3 x^{3}-4 x+4$$

For this item, you need to list all the possible rational zeros for the function. So please recall that that means we're going to list all of the factors of P and divide them by the factors. Q. Let's also recall at P is the final constant, that is, er, if he in queue is the leading coefficient. So let's go ahead and list thes. And let's be mindful that we need to use the positive negative options in all cases. So if we list the factors of eight, you know I've got one on eight, two and four that exists. Exhaust that list. And then, of course, we have a leading leading coefficient of one, so we only have one in the denominator for the factors of Q. In our final list of possible rational zeros, it's positive. Negative. One, 24 and eight

This item asks youto list all possible rational zeros using the rational zero theorem. So let three call that involves listing the factors of P and dividing by the factors of Q. Let's also recall that P is the final constant in queue. It's the leading coefficient, so we can go through endless thes. Let's recall that we need to make sure that we include all positive and negative options. Directors of six are one, six 23 factors of three or one in three. We need to go through this list. We're going to write eat each term from the numerator over each term. The denominator. Let's see if we have any duplicates after that. So we've got one over one Tuller one three over, one six over one. Now we'll go along and we'll use the three won over three to over three three over three, six over three. We could do some reducing here. Um, so here we know we have a one two, three, six, 1/3 2/3 one in the three. So our final list would be the list without duplicates. So we have the positive negative one that takes care of this one and this one I'm gonna uh and then we've got to. Well, sit. We have a 33 occurs twice. Here. We have the six. We have 1/3 into 2/3. And there you go. That is the list of all the possible rational zeros.

For this item, we will find all the possible rational zeros, and we will use the rational zero therapy. Let's recall that the rational zero theorem asks for the factors p divided by the factors of Q. Let's also remember that the factors of Pee Pee is this final constant in Q is the leading term coefficient. Let's also recall that we need all positive negative factors. We've got 15 so I've got one, 15 three and five and the factors of the Q term. Which is, too, if get one into and in turn, we need to express each numerator each term in the numerator over each term, in the denominator. So we'll list thes through so that we can be totally transparent about our work maker thinking visible. And normally, when we get to this point, we go through and we check to see if there's any redundancy. Any duplication amongst all of these factors in there knocked. So this right here, this set of eight times to 16 different values completes the list of all possible rational zeros for the given function

This item asks you to find all possible rational zeros but the given function and to use the rational zero the're, um while doing so therefore, we're going to find all the factors of he you'll divide. All those factors are the factors of Q. Let's remember that the final constant is the pea Turn in the leading coefficient is the queue. So we begin by making sure that we include positive negative for all possible factors. Factors of six will have one, six, two and three factors of four. Well, if one for into and we need to go through and we need to list all possible combinations of numerator Sze over denominator. So we have one over one. Let's of course, recall. We've got our positive negative one over one to over one three over one six over one to over one. I'm sorry. We already had that, don't we? So we went through and we listed everything over one. Now we're going to list everything over to one over two to over two three over two, six over too. Now again, we're gonna go with with each term each factor. I'm sorry. From the numerator we're going to list them all over four. Went over four to over four. Three over four. Six over four. Gonna finalize this list. We definitely have a one. There's only 11 there. We'll have to. We will have. I was looking to see if we have another two. I don't believe we have another value of two. We have a three. We have a six now. We'll continue and make sure that we don't have any duplication. So we've got a 1/2 that's new to over two was a one. We already have that three over two or one and 1/2. Six over two is three. We already have that one on four is new. Tool before is one have equivalent. We already have that. 3/4 is new and six over four would be three over toothy equivalent. We already have that. So here you have your complete list of possible rational zeros for the given function.


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