Question

Can anyone explain how to factor this?

Answer 1

can you factor quadratics ?

Answer 2

you'll get a quadratic by plugging in x^2 =y

Answer 3

first you exchange x^2 with t
now you have: \[-6t ^{2} + 18t + 24 = 0\]
now extract -6 in front of the equation:
\[-6(t ^{2} - 3t - 4)\]
now take the -3t and divide it into two parts, so you can combine numbers in the parenthesis two by two. because the last number is 4 one of the parts of -3t must have four in it. in this case, -3t = -4t + t
\[-6(t ^{2} - 4t + t - 4)\]
now you group them together, t^2 with t and -4t and -4
in the first case, you extract t
in the second case, you extract -4
\[-6\left[ t(t+1) -4(t+1) \right] = -6 [(t-4)(t+1)]\]
now return the x^2 instead of t
\[-6(x ^{2} - 4)(x ^{2} + 1)\]

one last step, you can write (x^2 -4) as (x-2)(x+2). when you do that, you have your solution;) if you don't understand, feel free to ask

Answer 4

This is a reducible quadratic. If you take out the common factor of -6, then let u = x^2
Then you get \[-6x^4 +18x^2 +24 = -6(x^4 -3x^2 -4) = -6(u^2 - 3u - 4)\]
where u = x^2 for ease.
\[-6(u^2 -3u -4) = -6(u-4)(u+1)\]
Then substitute u = x^2 back in:
\[-6(u-4)(u+1) = -6(x^2 -4)(x^2 +1) = 6(x+2)(x-2)(x^2+1)\]
I used difference of two squares to get the last part.

Answer 5

to both of you, @mww and @stijena , i really appreciate you helping people, but giving entire solution at once will not help him learn how to solve the problem by himself/herself. You see, this is learning site and not answering site. So, i would like to request you both to engage him and make him reach the correct answer! thanks :)

Answer 6

thanks a lot. her* not him.

Answer 7

oops , sorry, *her *herself

Answer 8

well, it is up to her to decide whether she is gonna copy the final solution or engage into solving the example.
I haven't just said the answer is A; I tried to explain every step in the process of solving it and encouraged her to ask further question if she doesn't understand some part. also, I left out the final form of the solution, letting her assemble it.