Solving for x? Check my answer?

Question

anonymous · Answer

Leaning towards B but I'm not sure :/

directrix · Answer

Just a moment. I'll check to see if I'm leaning towards B, also.

directrix · Answer

We have to account for 5 roots.

directrix · Answer

I'm leaning towards option B. Let's see what the others crank out as solutions.

jhannybean · Answer

$$x^5+x^4-7x^3-7x^2-144x-144=0$$$$x^4\color{red}{(x+1)}-7x^2\color{red}{(x+1)}-144\color{red}{(x+1)}=0$$$$(x+1)(x^4-7x^2-144)=0$$

jhannybean · Answer

I'm up to that step right now. Do you see how I did that?

jhannybean · Answer

I simply grouped each of the two terms together, and factored out the common terms between each group.

jhannybean · Answer

Now for $x^4 -7x^2-144$, let $a=x^2$. With that substitution you will have $$a^2 -7a-144\implies (a+16)(a-9)$$

directrix · Answer

That is an impressive application of factoring and is simpler than the Rational Root Theorem.  @Jhannybean

jhannybean · Answer

She just wanted the answer -.-

jhannybean · Answer

Thanks for giving it to her @Directrix

directrix · Answer

@Jhannybean  I said where I was leaning; not where I landed.
And, I complimented your work.