Question
In Problems $9-18,$ tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not.$$5 x^{2} y^{3}$$
In Problems $9-18,$ tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not. $$ 5 x^{2} y^{3} $$
Answers
In Problems $9-18,$ tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not. $$ 5 x^{2} y^{3} $$
Okay, So to start this question, we can think about what exactly a mono meal is and what it needs to include in order to be considered a mono meal. So over here, um, we have that amano meal is a product of a constant and a variable, and that variable is raised to a non negative integer. Okay, Um, look at the general form of the Manami. Over here we have a times X to the K where X is a variable a is the coefficient, and then K is the degree. So if you look down at the problem, we have to Exe cute. Now, at first glance, we see that it's a product of a constant invariable, so that, um, checks out. And then we have that the variable is raised to the power of three, which is indeed a non negative integer So this doesn't violate any of the qualifications of being binomial. So yes. Um, this is a Manno meal, and then we just have to identify the coefficient, the variable and the degree. So, looking back up here, we know that the variable, um, in the general form of X and we also have X here. So are variable is X Um we look up here at a ese coefficient. We look back at our question, are coefficient is too. And then once more we see that in the general form K is the degree. But if we look back at to execute, we see the K is represented by three sore degree of this mano meal is three.
So here we're tasked to find if negative for X squared is a polynomial. So the way we have to check that is to analyze the term of this Monem you as long as this non negative and it isn't manager than it is a mono meo instance to is both not negative and an imager Negative four X squared is a mano vio So the code fishing of this term would be negative four the variable being X and the term as after mention would be to
Okay, So, um, to identify this expression eight over X is a mono milk. First considered what, um, the next person needs to have in order to be a binomial, so we need to be a product of the constant and a variable. Um, and then we also need to be raised to a non negative imagers. So if you look at the general expression of amano 1,000,008 times extra Que, where is a coefficient extra variable? And then K is the degree. So looking at our, um, expression here we have eight over x, and we can do What we can do is we can manipulate this a little bit. Um, this is actually evil, too. Using our properties of exponents. This is equal to X. Excuse me eight times X to the negative one. No, this is indeed a product of a constant invariable. We have eight times X to the negative one. However, as we brought the axe into the numerator, we can see that the, um, the exponents here is actually a negative value. So this is not a mono meal
So here we're trying to find a native to X to the power to native three is a mono meal or not. So what we should look at in these problems is the degree of the expression. And in this case, the degree is negative. Three. So for a mono meo, the degree has to be both non negative and an imager Negative three is negative. Therefore the term is not a mono meal.