factor-each-expression-3-x3leftx23-xright2-15-xleftx23-xright2-2

Question

Factor each expression.
$$
3 x^{3}\left(x^{2}+3 x\right)^{2}-15 x\left(x^{2}+3 x\right)^{2}
$$

Amy Jiang · Accepted Answer

Okay, so we see that we have an X squared plus three x to the power of tune common. So it&#x27;s like factoring that out. So we&#x27;re off off a three x cubed minus 15 and then between These determines we have a three accent common to attract that out. And it&#x27;s also notice that&#x27;s, um, between this factory. We have an X in common. We contract that out to have a X Times X three that&#x27;s squared, and then we have a big factor out of three ex. You get eggs squared minus I&#x27;m 15. Divided by three is fun. Okay, so we can bring in our power here. So we get X squared expose three squared. And then we were three acts and an X squared minus five. Okay, so let&#x27;s simplify what we have or combine like terms. We have X Times X squared times X. You can rewrite that as three x cubed exports three into part two, an X squared minus five

James Kiss · Answer

When thinking about applying the greatest common factor to this expression, you got to think about taking out the smaller one. So you need to think, what smaller between? Negative 2/3 of negative 5/3 in its negative 5/3. So your greatest common factor, X squared plus three to the negative 5/3 out. And now what&#x27;s left over would be X squared, plus three. To what power? What power is going to take us from a negative 5/3 to a negative 2/3? That would be 3/3 or just one. So we&#x27;ll leave this as just expert plus three, and then we&#x27;re gonna add to that one because we took out this term were dividing this term out. We&#x27;re left with one in parentheses. Now do a little bit of cleaning up here. This is equivalent to expert plus three to the negative 5/3 times X squared plus three plus one, which is expert before No, we have a negative exponents. So this is equivalent to X Square plus four in the numerator. And there&#x27;s next opponent property that says when we are raised to a negative power that it can go to the denominator and then negative power now becomes positive. We can also think of exploited plus four as the cube root uh, X squared plus three to the fifth. We can break Carter that down since five is greater than, Ah, the erratic and three. Let&#x27;s think of this as the cube root of X squared plus three to the third. And we&#x27;re still left with X squared plus three squared. Now we can evaluate this experience plus three cubed under a huge route. It would just go to the, uh, in front so that would look like X squared plus three to the first of its evaluated times. The cube root of X squared plus three squared. And that, my friends, is complete.

Ramzi Deek · Answer

so we have X cubed minus three X squared plus X minus three. So lets start grouping here, so x cubed and x so x cubed plus X minus three X squared minus three. So it&#x27;s factor these two. Then factor these two so X cubed the next. Let&#x27;s take Excel so I will be X squared. Plus one x into X squared plus one. Let&#x27;s take negative three out for the next expression, so it&#x27;ll be minus three into X squared, plus one so X squared, plus one times X minus three. That&#x27;ll be your factored expression.

James Kiss · Answer

way. Want a factor? X Cubed plus three x, where we can take out the greatest common factor, which is X squared and would be left with X plus three.

James Kiss · Answer

we can factor out an X plus three to the 1/2 from each term, leaving us with one minus X plus three. And that would be to the first power because we would have liked bases. And then powers of 1/2 added with the power of one gives you your three halves and then a little tweaking from here explodes three to the 1/2 distribute that negative is one minus X minus three. A little more tweaking. Combining are like terms exposed. Three of the one have would be negative X minus two. A little bit more tweaking. We could say Expo Street of the One hat What&#x27;s factor out? A negative one. So it&#x27;s time to negative one to the X Plus two. And finally, we could say Negative. Let&#x27;s bring that negative one right out front. Let&#x27;s turn our experts really the 1/2 to the square root of X plus three. That&#x27;s equivalent Times X plus two final answer

Sarah Brown · Answer

All right, So we are given the expression three execute plus three X squared minus X minus one. So, to factor this, we have first heart decide what is our best approach. So what? This problem here, your best approach is going to be to group yourself. Okay, so then now that we have that we&#x27;re gonna set up our two groups. So we&#x27;re gonna set that bar groups. My first group is gonna be three x cubed plus three acts squared. And then my second group is going to be a negative. X might swell. All right, so then, now that I&#x27;ve done that, my third step here is going to be to factor out your g c f. So, in doing that between three and three much, my grace UCF this three and then with X cubed and X squared, My grace form factor is X square, the lowest exponents So that now I have to figure out the in between every disease. So I have three x squared times. What gives me three x cubed. Just one more X and three x squared times. What? Give me three x squared. Just one. Okay, so now we&#x27;re going to go to our second set of parentheses. So between negative X in minus one. What? Is there Grace going back? So the great want doctor here is just a one. Now, we don&#x27;t want this first term to be negative, so we&#x27;re gonna also plot a negative here. Okay, So now we&#x27;re gonna find the inside of this front sees so negative one times. What is negative X Justin acts and negative one times. What is negative? One A positive. So now that we&#x27;ve factor those out now we&#x27;re going to find our chill factors of the expression. So to make sure that we can&#x27;t even find the factors we have a check to make sure that are parentheses are the exact same. They are some means that I can factor this expression. So one of my factors is going to be what&#x27;s inside of those prophecies. So I only read it once. Hey, that&#x27;s my first factor. And then my other factors going over the GC efs. So I have three x squared as my first and my second jeezy f I have a minus one. So the X plus one and three x squared minus one are your fact

Problem

Factor each expression. $$ 6 x\left(x^{3}+7\rig…

Problem 51 Hard Difficulty

Factor each expression.
$$
3 x^{3}\left(x^{2}+3 x\right)^{2}-15 x\left(x^{2}+3 x\right)^{2}
$$

Answer

3$x\left(x^{2}-5\right)\left(x^{2}+3 x\right)^{2}$

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

Finite Mathematics and Calculus with Applications

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Kayleah T.

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3$x\left(x^{2}-5\right)\left(x^{2}+3 x\right)^{2}$

Finite Mathematics and Calculus with Applications

Catherine R.

Kayleah T.

Caleb E.

Samuel H.

Vectors Intro

Vector Basics - Example 1

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

Catherine R.

Kayleah T.

Caleb E.

Samuel H.

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

Finite Mathematics and Calculus with Applications