in-27-39-factor-each-polynomial-completely-x4-16

Question

In $27-39,$ factor each polynomial completely.
$$
x^{4}-16
$$

Bahar Tehranipoor · Accepted Answer

this exercise is one of factors, all normal. So one thing when you start a factor law is that you will recognize when you have something squared minus a perfect square. You can always write it as he squirt of first term minus the square root of that second term times this world 1st 1 plus, whereas I&#x27;m so says a bit confusing. But we can write this as, uh, ex fourth, actually, forthe money. 16. Hit the square of exit polls. Six squares. We have X squared. This sort of 16 is going to be forced with extra minus four times Expert Plus, for now, it could be really easy to say all this answer, but that would not be a complete answer because it&#x27;s us. Two factories polynomial completely and X squared minus four can also be written using that trip. It&#x27;s a term squared, minus another term squared, uh, buy rating it as sort of back sort of X square before, which is to sow X minus two times X plus two and then you can&#x27;t factor Expert was for so that would be 1/3 term. And that is factoring is pulling more graffiti

M S · Answer

So you want to go back to his polynomial? So excellent. A fort to minus 80 mine is called a difference of squares. A difference of squares is when you have perfect square here minus and of a perfect square. So it&#x27;s a factor of this. He would just take the square root of the first term. So the square root of exit support is exit a second and this period of anyone would give us an I. So we&#x27;re gonna have X squared plus and I times x squared minus night. All we do is take. Like I said, take the spirit of this first sermon and swearing in a second term, and you&#x27;re gonna have plus in the middle and multiply it by minus in the middle. So I&#x27;m gonna re for you to show you exactly what happens. So first X to the port outer minus nine, x squared inner plus nine x squared And then negative nine cents Files of nine will give us negativity would. So this positive nine this negative nine in the middle goes away. Ever lift with extra? The 4th 1 is 81. So I just wanted to show you that the difference of squares is when you have that Plus in that minus. But you have the exact same numbers, but the plus and the minus in the middle. It makes a difference because it makes this middle terms here, counselor. So he factored into X squared plus nine times X squared, minus nine. And as you see, we can factor again this term here cause we have a perfect square here in a perfect square here. So our first ever state of saying, because the difference of squares, it has to have a subtraction sign in the middle. All this plus sign it cannot have. The blessed on it is like that. You cannot back further. But this second term, we&#x27;re gonna take the square root of picks, which is gonna take the square root of X squared, which is X, and it&#x27;s great of nine with just three. So we&#x27;re gonna have expressed three times X minus three. In essence forest

Bahar Tehranipoor · Answer

here. You want a factor? This poor animal completely. So the one thing I know this is that there&#x27;s an excellent of return, some things we could really easily just taken x out. But before we do that, let&#x27;s also see if there&#x27;s anything else I will take out easily. As you become better looking at these questions, you&#x27;re going to see you very easily those two that we can also take out. So a two is common all these terms. So if we take out a two ETS will have out of four X cubed A to X square left and 10 x squared. We&#x27;re going to have a minus five x left and first XX would respond to have history. Now we want to focus on factoring this to expert minus five X was three. Hey, this was actually a question that we&#x27;ve done in this chapter before, but this will throw it again. So what we&#x27;re gonna do is first with that constant and against the moon into it&#x27;d look at that causes it free. Um, have a two in one of the experts we were gonna have to write as to x X, because this is a positive and the coefficient of X is negative. We&#x27;re going to have some sort of combination of your two x plus two x minus and then x with the opposite sides. So with three, really only write it as three times one. So let&#x27;s just try something like minus three plus one. And, of course, in my head, I already know it&#x27;s going to work because, as you see it more Oh, sorry, my bad. That actually won&#x27;t work because you have a negative consequence. So rushing, actually Republican through the wrong answer. But if that&#x27;s what the negative three would have been the right answer. But you actually want keys to both be negative, because for me it is positive. So I take that back. That will be a negative, and then it will not be this one. And during this way, because that will give you a bit of seven. It&#x27;s so it&#x27;s really used to make the steak, and I will sit here and say that Yes, I made mistakes, so we have a minus one hair and a minus. We&#x27;re here because that will then give you two X squared minus two. It&#x27;s minus three exits give you the negative five X plus three. So you see, even as you get faster, it still will be easy to make the stakes. So our final answer would you do that? To expect down is just going to be right here.

M S · Answer

so one of factors polynomial completely so looking at days, he might have the urge to distribute this negative into this factor here. However, we cannot do that because we have square here. So that squared means we&#x27;ll have four minus. Then why? Minus one times why minus one. So I&#x27;m gonna go ahead and boil. So we have four minus and then we&#x27;re gonna was apart the first term. So what time is what I would give us what&#x27;s weird out here? Negative, Woz. Inner negative. What? And in the last, which gives us plus morning, I don&#x27;t have what four minus Why squared minus two AA plus one. And now what? Understood me. Just negative. So four minus y squared plus two. Ah, then minus would. So in every distributor, negative really just changed all the signs. So become blind like terms will have negative y squared. Plus two. I close three someone to bring this over here so no one needs a factor This turn so unused to split apart this middle time so that we can factor by grouping. So we need to take our coefficient in our last term. Most apartment together and negative one times three. Is this negative? Three. They would take our middle term and we need the numbers to add some positive too. The list of backers of 313 But we know that one of them needs to be negative. So we make one negative, then three minus one gives us positive, too. And that&#x27;s exactly what we need. We&#x27;re gonna split apart or middle turn. They will have negative wars squared minus one. Why? Plus three. Why? Remembering down this plus three here. So no need to get these two terms and angry thes two tarts. The universe pair. We get back throughout a negative. Why and only inside we&#x27;re left with why, plus one, they&#x27;re going to second pair. We can factor out of plus three and will exploit the water plus point. No, no, we&#x27;re on the right track when this storm equals this term. Still have brought a plus one and then negative wide plus three. You know, we could rearrange the second factor to say three minus y if that makes you feel guilty and I would factor complete

Bahar Tehranipoor · Answer

and discretion gonna factor this. Paul knew completely. So we have X squared Y minus 16 1 So what? Something like this, I always get a little thrown off by seeing an ex and why that&#x27;s pretty normal. But let&#x27;s kind of just break this down, do it the way that we would when we first started instead of just intuitively kind of looking at it and see first, is there anything that we can take out from both of these terms? And there? Is that why, you know, it&#x27;s kind of weird to look at having both. That&#x27;s why you can&#x27;t just take that line out. That kind of simplifies it a lot. So we have Wyatt Times X squared minus 16. You know that expert minus 16 isn&#x27;t gonna be talking about Locke in these past few videos? Is that when you have some terms squared minus Elektrim squared? You can&#x27;t just write it as we&#x27;ll show you why Times take the score to the first term X squared the second terms force we have except minus four and X plus four. So I don&#x27;t really say why this works, but if you just kind of look at it. You get X squared plus four X minus four X that, uh, exit the first power turmoil. Cancel just what you want and you will get that minus your perfect square to this case is 16. So that is how you factor this point on you.

M S · Answer

so he wants a factor. This polynomial completely. So the first thing I notice is that we have a common Manami o of X here, here, in here. So I want a background in X. And whenever we backed out of mono meal, we always factor out the lowest degree. So in this case, just exit the first, which is just six. So they will have two x squared less 13 x plus 15 left. So now we can factor what&#x27;s inside the parentheses. So we&#x27;re gonna take this first term coefficient multiplying bar last time in two times 50 will give us 30. And we wanted to add to our middle term in this case, 13. So the list the factors of 31 in 30 soon scene three in tune and five and six because this 13 is positive. All both of the terms in the payer has to be positive. So this is our question, because one place starting starting line two plus 15 is 17 but three plays tennis 13 So that gives us the pier that we need. It&#x27;s analogous. Split apart on middle turn. So we still have X, and they will have. I&#x27;m gonna use big markets here, but they will have two x squared and we split apart of mental term. So plus 10 IX, close three X and then bring known at plus 15 here to know any degree barbers to terms and then grouper Last two terms. So he&#x27;s back throughout from our first factor. We can factor out too, because God is coming back to between suing San is too. They&#x27;re looking also back to our necks. Cyril it with six plus five on the inside. From the second factor, we can factor out of three really put expose five on the inside. So now we&#x27;ll have X. And because we have the same term here in here, we know that explosive five is a factor and they will bring down what&#x27;s left to explosive three and we factor in complete

Problem

In $27-39,$ factor each polynomial completely. $…

Problem 33 Medium Difficulty

In $27-39,$ factor each polynomial completely.
$$
x^{4}-16
$$

Answer

$(x-2)(x+2)\left(x^{2}+4\right)$

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Algebra Educators

Grace H.

Catherine R.

Kayleah T.

Maria G.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Kayleah T.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Additional Mathematics Questions

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$(x-2)(x+2)\left(x^{2}+4\right)$

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Kayleah T.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Catherine R.

Kayleah T.

Maria G.

Ann Xavier Gantert

Algebra 2 and Trigonometry