factor-each-expression-x2-x52leftx2-4right-1-22leftx2-4right1-22-x5-2

Question

Factor each expression.
$$
x(2 x+5)^{2}\left(x^{2}-4\right)^{-1 / 2}+2\left(x^{2}-4\right)^{1 / 2}(2 x+5)
$$

Amy Jiang · Accepted Answer

Okay, We&#x27;ll do what we have in common. So we have a, um you exposed by coming as well as an X squared minus 4 to 5 1/2 in common. So let&#x27;s factor. Is that so yet fallen. Okay, so what we have remaining is an X Times two X. That&#x27;s fine on the next word of minus four, the heart of negative one and then plus two time. What now we get the following.

Amrita Bhasin · Answer

we know we can split up five acts into four x plus X, therefore giving us negative acts times X minus for lost X minus four, which simplifies to negative X minus one times X minus four.

K B · Answer

So here we have extra fourth minus five X squared plus four. And we can factor this as squared minus four times. Expert minus one of me Got this because native one time negative Force four and negative four minus one is 95. So maybe five and positive for

Aditya Sood · Answer

Hello, everybody. Welcome. We want to factories, expression X squared plus five x plus. For so when factoring, we can either use the quadratic formula or we can use this nice trick. I&#x27;m gonna show you. Um, and it doesn&#x27;t work all the time, but it does work from a lot of the problems. So the trick ensuring you is that we want to find two numbers from that, add up to five and multiply up to four so that adhere and multiply here. So let&#x27;s think of some numbers that could do that to numbers that could do that. So we&#x27;ve got four and one because for plus, one is to go to five, so they add up to five and four times one, they multiply up to four. So now we&#x27;re gonna use that. We have got expert, and we&#x27;re gonna break up five X using these numbers for X plus X Plus four. And the reason we did this was because, uh, the two numbers that we used our foreign one, right, So four. And we&#x27;ll exit. Just saving his one excuse about foreign one. Um, so now that we have it that broken down, we can actually factor this. So we&#x27;ve got X the X plus four into one into X plus four. Right. Um And now, since extras for is common in both sides, we could say this is equal to X plus one into X plus four. And there we have it. Guys, um, we have our expression. In fact, it form. Thank you for watching. And I hope this helped.

Angela Guo · Answer

the first thing we&#x27;re going to do here. This factor out the negative one because we want our leading coefficient to be positive. So who factor on the negative one? This is now going to be a positive to X before minus the X squared y skirt. Linus five white it before and now we can take her age, which is positive to multiply of our C, which is negative five. So this will give us make it a 10. No, no, we want to find two numbers to introduced on Multiply together to be negative 10 and add together to be negative. So that&#x27;s going to be positive to negative. So that means we are going to be right this and break down that middle turn with two turns plus well excluded y squared minus hi ex square by square And next we can start, um, factoring by grouping. So from the 1st 2 turns, we are going to factor out new X quick and we&#x27;ll be left with X squared plus y squared from the second term. We can factor out the negative by why square and that is going to, uh, give us X squared plus y squared. So that means this can be factored into negatives. X squared, plus y squared times. Do you like, squared minus my voice work?

James Kiss · Answer

we first want to think about greatest common factor. And we&#x27;re gonna take out the smaller wand, The smaller ones, actually, the negative 3/2. So we&#x27;re gonna greatest common factor X plus five to the negative three halves. And then we&#x27;d be left with X plus five. We need to be thinking about what power do we put your So we can get this negative 1/3. Add to it to get negative 1/2 and it would just be to the first. Okay, negative three halfs plus two halves. This negative 1/2. So experts five and then minus one. So if we were distributing this, we would get the expression above. All right, clean this up a bit by combining our like terms in the parentheses. So x plus five minus one is the same X plus or no, um, this is the same thing, since we have a negative exponents that can go to the denominator X plus fours in the numerator, and we&#x27;d have X plus five to the power of a positive three halves in the denominator. This is the same thing is X plus for over the square root of X plus five to the third. This would be equal to experts. Pore over the square root of experts. Five multiplied by itself three times. But what if we go to and won the reason being? No, This squared is going to be counteracted by the square root. So is going to get evaluated. OutFront Final answer would then be experts poor over X plus five times the square root of X plus five

Problem

Factor each expression. $$ \left(4 x^{2}+1\righ…

Problem 55 Hard Difficulty

Factor each expression.
$$
x(2 x+5)^{2}\left(x^{2}-4\right)^{-1 / 2}+2\left(x^{2}-4\right)^{1 / 2}(2 x+5)
$$

Answer

$(2 x+5)\left(x^{2}-4\right)^{1 / 2}\left[x(2 x+5)\left(x^{2}-4\right)^{-1}+2\right]$

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$(2 x+5)\left(x^{2}-4\right)^{1 / 2}\left[x(2 x+5)\left(x^{2}-4\right)^{-1}+2\right]$

Finite Mathematics and Calculus with Applications

Catherine R.

Anna Marie V.

Kristen K.

Joseph L.

Vectors Intro

Vector Basics - Example 1

Margaret L. Lial, Raymond N. Greenwell, Nathan P. RitcheyFinite Mathematics and Calculus with Applications

Catherine R.

Anna Marie V.

Kristen K.

Joseph L.

Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Finite Mathematics and Calculus with Applications