in-3-8-write-each-polynomial-as-the-product-of-its-greatest-common-monomial-factor-and-a-polynomia-3

Question

In $3-8,$ write each polynomial as the product of its greatest common monomial factor and a polynomial.
$$
5 a b^{2}-15 a b+20 a^{2} b
$$

Bahar Tehranipoor · Accepted Answer

in this exercise, we want to write each polynomial as a product of its greatest common mental male factor in a polynomial. So as all these questions go but I like to do first is look at each term separately, kind of break it down into its parts and then see what is shared by all these. Because that&#x27;s how we&#x27;re gonna find the G c d. And then we factor that out will be left with that polynomial so that we could write that product. So let&#x27;s first look at this first term. So five a B squared. How do we write that? We could write that as five times a day, taking B squared. I just be tongues be so yes, we have Now, this wouldn&#x27;t go that negative for now. But we have this 15. Maybe we&#x27;re going to write that will have five times three breaking 15 down into it. Uh, prime rib. Cornish is five times three. Then we have times a times B and then we have our last term. Just write that minus here. Let&#x27;s hear that last term we have 20 which we can break down into two times. Two times five a square. So eight times a day and then one be termed sometimes be so here. Now that we have broken all this down, I&#x27;m gonna go in with the green, and I&#x27;m gonna highlight everything that is the same between all of themselves. Look at that five. Does each term ever vibes were five here, five here in a five year. So we did. How about a We haven&#x27;t a here and a here and then a here. How about a B? We have to be here of the here and maybe here. So you having second B? But as we can see, that is not gonna be shared by all of the components, because this is the only term that&#x27;s gonna have that B squared. So this part is not gonna be part of the product that we&#x27;re going to write. So we have five baby fire, baby fire, baby, that is shared by all means. Let&#x27;s take it up. You have five a. B. That is gonna be our g c. D. Now, to write the polynomial part of the product, we&#x27;re gonna look at basically what wasn&#x27;t underlying so in this part&#x27;s be in this part we have minus just 30 minus three and then this part. We have this two times, two times a so two times two is 44 times ages for a plus for a and it&#x27;s as simple as that.

Bahar Tehranipoor · Answer

in this exercise we want to write. This polynomial is a product of its G, c, D or the greats. Common Minimal factor and a pollen. No note. So I keep saying Do CD, But what? I mean, it&#x27;s just that greatest common factor and we were gonna find is really similar to how we would find a new CD. So to write this product, what I like to do first is just break it down into the individual terms. So all right, each one, basically kind of just as a product of the things that make it up. And then we&#x27;re gonna go from there. So let&#x27;s see first of this for a term. Very simple. We break that into is for Time&#x27;s A, but we can actually break four down a little bit more. So let&#x27;s write as two times two times a day that we have a minus 12. Maybe we can write as breaking 12 down into two times two times three times a times B. Then we have plus 16. A squares of 16 is four squared or two to the fourth. We have two times two times two times two time&#x27;s a time. Zach So now that we have done this part, easy part is just going in with the green. And we&#x27;re going to underline everything that is shared by all the terms. So let&#x27;s start with this to to there&#x27;s a two Here is also a to here. How about a second? Two? We have a two here. A 2nd 2 here at a second to here. Who is it? How about a so a We haven&#x27;t a heaven? A You have a name now. None of these other terms are going to be part of that 10 no factor. Because Foray is the term with the, uh, least basically amount to it. It&#x27;s kind of weird to phrase like that, but it just has two times, two times a day. So there&#x27;s nothing else that could possibly be a part of the factor. So we know that for a is going to be that greatest comment when real factors well, for a and then we&#x27;ll just basically look at what we didn&#x27;t underline and that&#x27;ll be the polynomial part of the product. So taking a foray from for a we just have one left now looking at what we don&#x27;t have underlined here. We just have this three v So minus three B. Make sure you don&#x27;t miss the sign because that could be pretty easy to forget. So we have minus three b. Then here, let&#x27;s see what we have left. We have a two, a two, and a so that would be four eyes we have plus four a. And it says is that that&#x27;s your answer.

M S · Answer

so we want to write. This polynomial is a product of the greatest common monem you&#x27;ll factor and a polynomial. So the greatest common Manami all factor is just the greatest common factor that includes a variable. So we&#x27;re looking for our greatest common factor and it&#x27;s the same as if we did not have variables here. So one look at our regular numbers 63 and nine. The greatest comment back there between these will be three. Because we always wanna we look at our lowest number. If you wanna see the factors of three are 13 The factors of six are 123 and six in the factors of nine are 13 and nine and the only home in factor is 33 and three. So we know we&#x27;re gonna factor out of three. Now, when it&#x27;s looking at our variables, we have eight of the 4th 8 and 1/3 and a square. And whenever you want to find a comet back to of variables is always the lowest exponents. So it&#x27;ll be just being three. A squared was always a Lois. Explain it. So we&#x27;re back to just out and my factor out that just means divide out. So we took our first time six day to the board, and we want to see what can we multiply? Three. A squared by to get our original so three times what is sticks? And that&#x27;s two in a square times what to say to the fort. And since we add exponents, that army a squared and we wouldn&#x27;t do the same thing to our middle term. So three times what is negative? Three. And that&#x27;s negative points and a square times what gives us a cube, and it&#x27;s just a. And then we do the same thing for last term three times. What is nine. And it&#x27;s three and a square times what it gives us a squared and that let things so we don&#x27;t have a variable here. So this is how it correctly used the greatest common with no meal factor and a polynomial

M S · Answer

So we have X cubed times y cubed minus two x cube y squared plus x squared y squared. So we want to write. Each polynomial is a product of the greatest common mano mule factor in a polynomial. So basically thank greatest common factor, but we have variable sale. So first I wanna look at our coefficients, and in this case, it&#x27;s just one negative two and one. And the greatest common factor of this would just be one, so we can&#x27;t really pull out a regular number. So now we&#x27;re just gonna look at our variables. Parcels. Look at it whenever you factor out the greatest column. In fact, dirt of the variable between multiple common is always the exponents, the lowest exponents. So in this case, we have X cubed, X cubed and X squared, and it&#x27;s always the lowest. Exponents are gonna background and X squared in the same thing with our why we&#x27;re gonna back about the lows exploded. It is gonna be why Square, Because two is lowered in three. So factoring this out and my factor out, it just means divide out. So now you want to actually. So, between all three in this China mule. So we&#x27;re gonna do the 1st 1 first. What can I multiplied by X squared to get X cute? And because I&#x27;m at the exponents two plus, what is three units? Just want challenges me x And why squared times What gives us? Why cubed? And that&#x27;s just why because well, at those exploded, I wonder the same thing with our middle. So because we pulled out basically a one x squared, we need to say one time what is negative, too? That&#x27;s negative, too. X squared times. What is X Cube? That&#x27;s just X and Y squared times what gives us by squared. And that&#x27;s nothing. So we just leave that rendered same thing with our last term X squared times. What gives us X squared? Yeah, that&#x27;s nothing in West great times working since y squared. And that&#x27;s nothing. But we can&#x27;t just not put anything here because then we won&#x27;t multiply. We won&#x27;t get that last term. So we have to put plus one and you can prove all of this by distributing it back. We can check so you can say this is our answer here, but we can check to make sure so X squared times X 70 must execute. Why squared times? Why give us why cubed mine is too to close. One is three and we don&#x27;t have a light turn. So I squared plus and then just x squared foot, not plus X squared times y squared If you see that gives us our original equation.

Bahar Tehranipoor · Answer

in this exercise that says We want to write This polynomial is a product of his greatest common binomial factor in a polynomial. So let&#x27;s look at this and see what can we take out. That&#x27;s what I like to think of when I think about factoring is almost like what is something as air saying that is common between both of them were looking for the greatest one, and how can we just take that out? So it almost simplifies what we&#x27;re looking at. So here we have a term of eight X squared and 12 X. So let&#x27;s kind of look at these individually first, how could we write eight X squared? We could take this eight and right as two times two times two. Of course, we have Tom&#x27;s ex Times X for a first term for a second term of 12 x, so we can write that as taking 12. All right, two times, two times three times X. Now let&#x27;s look at both of these and see what is the common factors between them. So, of course, they both have one, too. They both have two twos now. Eight X, of course, has the other two. That is not uncommon with 12. So let&#x27;s get that. We both have one X. Now it expert has another ex, but again, that&#x27;s not common between both of those. We won&#x27;t look at it. So let&#x27;s extract what we have just found the same. So the green colors will be two times two times x. So that is for XO four X Is that greatest common? More? No meal can pronounce the word factor, and that is the first part of the question. So now we have a polynomial left over when we take this out. So if we factor that out, let&#x27;s look at our first term first for Take four x out of X rayed. We can even look at what we didn&#x27;t underline here, so that would be a to an ex would have to ex. Now, if we look at 12 x, what we didn&#x27;t highlight was just three. So I&#x27;ll just read it again. Or answer will be our G CD, which is four X times. When we factored out. We have this polynomial, which is this two X who&#x27;s three, and it&#x27;s as simple as that

M S · Answer

So we have 21 a squared plus 14 A plus seven. So basically, we want a factor out The greatest comment back Doon. But in this case, we have monitor. We have modern meal terms, so we need to factor those out too. So, looking at all three coefficients, we treat this as regular numbers and we want it back throughout the greatest common factor. So the factors of seven are one in seven. The factors of 14 you are one, two, seven and 14 in the factors of 21 are 137 and 21. So if you look and see, we have the greatest human factor of seven. So, in fact, you&#x27;re out of step in. Then we also want to look at all three terms and look and see what mon amigo, we can pull out. But not all three times have an a associated with it like this. Seven does not have in a here, so we can not factor out uh, variable. So now I just wanna act ourselves seven times. What gives us 21 ace Weird. And that&#x27;ll be three a squared seven times. What gives us 14 a and that&#x27;ll be too, eh? And seven times, like gives us seven. And that&#x27;s one. So now we have expressed it as

Problem

In $3-8,$ write each polynomial as the product of…

Problem 5 Medium Difficulty

In $3-8,$ write each polynomial as the product of its greatest common monomial factor and a polynomial.
$$
5 a b^{2}-15 a b+20 a^{2} b
$$

Answer

$5a b(b-3+4 a)$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Alayna H.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

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$5a b(b-3+4 a)$

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Alayna H.

Kristen K.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Alayna H.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry