PLEASE HELP!! factor the following completely: 8x^4-6x^2-27

Question

anonymous · Answer

Take $x^2 = t$ and then factor.

anonymous · Answer

$$8t^2  - 6t -27=0$$

chaise · Answer

x^2 = t
8t^2 - 6t-27
(2t+3)(4t-9)
Replace your t with x^2
(2x^2+3)(4x^2-9)

anonymous · Answer

can you please show me and explain the steps please? 
here is the equation again: $$8x^{4}-6x ^{2}-27$$

chaise · Answer

I will explain it for you :)
8x^4-6x^2-27
If we let x^2 = t we are able to factorise this equation VERY easily.
t = x^2
t^2 = x^4
8t^2 - 6t - 27 = 6x^4 - 6x^2 - 27; according to these restrictions>
8t^2 - 6t - 27 can be factorised to: (2t+3)(4t-9). Do you need help factorising?
Now we have the factorised version, we can substitute x^2 instead of t in this equation
we get:
 (2t+3)(4t-9) = (2x^2+3)(4x^2-9)
Do you want me to write this into equation editor so it's a little clearer?

anonymous · Answer

thank you for trying to answer my question, yes, the equation editor would really help. andi need a little help with factorising.

chaise · Answer

$$8x^4 - 6x^2 - 27$$
$$Let,t = x^2 and t^2 = x^4$$
$$8t^2 - 6t - 27 = 6x^4 - 6x^2 - 27$$
$$8t^2 - 6t - 27 = (2t+3)(4t-9)$$
If we were to expand $$(2t+3)(4t-9)$$
we would get: $$8t^2 - 6t - 27$$
Factorising is opposite to expanding. So we are just going backward to simplify the question.
$$(2t+3)(4t-9)$$
Now we have this equation we can simply substitute back in our t = x^2 and t^2 = x^4 into the equation.
$$(2x^2+3)(4x^2-9)$$
This is the fully factorised version of your function.

If you have trouble with factorising, have a look at some videos on factorising bionomials on youtube.

anonymous · Answer

thank you for your time and help. :D

chaise · Answer

Sorry if I made no sense at all.

anonymous · Answer

no, you made perfect sense :). i understand it now. ty.