Another stupid math problem... (1 Viewer)

[Brodie28]

Factorise X^5 - 9X³ - 8X² + 72.

Hence Solve X^5 - 9X³ - 8X² + 72 = 0


Im stumped...

 

[nick1048]

I don't see how that can be factorised. I was thinking the relationship between co-efficients and the roots. honestly, I'm stumped also, how do you factorise that?

 

[jm1234567890]

x⁵-9x³-8x²+72 = 0

x³(x²-9)-2³(x²-9) = 0

you do rest

 

[nick1048]

woah nice, different of two cubes and it all melts away, damn, will that be asked in an exam!?!

 

[jm1234567890]

it's a pretty standard question...

 

[nick1048]

ahhh crap. Takes a bit of first observation tho, thanks for the insight.

 

[jm1234567890]

ahhh crap. Takes a bit of first observation tho, thanks for the insight.

no problems, it all comes with practice

 

[Brodie28]

x3(x2-9)-8(x2-9) = 0

(X³-8)(X²-9) = 0

(X³-2³)(X²-3²) = 0

(X - 2) (X² + 2X + 4)(X + 3) (X - 3) = 0

X = +- 3

X = 2

Thanks

 

[Brodie28]

Yeah its standard.... I forgot that when factorising with 4 terms alot of the time it can be done in pairs...

 

[KFunk]

Jim's way is probably much quicker but if you don't have that hit of innovation then you can just use the factor theorem to find factors.

P(x)= x⁵-9x³-8x²+72
P(2)= 0
P(3)= 0

P(x)= (x-2)(x-3)(x³ +5x² +10x +12)

and so on...
P(-3)=0
P(x)=(x-2)(x-3)(x+3)(x² +2x +4)
=(x-2)(x-3)(x+3)(x+1+√3i)(x+1-√3i)

EDIT: Then I realised that it was the 3U forum... ignore the last line. What the hell am I doing answering a math question this late??

 

[jm1234567890]

Jim's way is probably much quicker but if you don't have that hit of innovation then you can just use the factor theorem to find factors.

P(x)= x⁵-9x³-8x²+72
P(2)= 0
P(3)= 0

P(x)= (x-2)(x-3)(x³ +5x² +10x +12)

and so on...
P(-3)=0
P(x)=(x-2)(x-3)(x+3)(x² +2x +4)
=(x-2)(x-3)(x+3)(x+1+√3i)(x+1-√3i)

yeah, use that if they give you bigger polynomials where factors can't be 'seen'

 

[nick1048]

awww fuck, I gotta revise my polynomials hardcore... Tomoro is another day nick!!!

 

[Will Hunting]

nick, Brodie's just pulling these from the Chapter 3 Challenge in Maths in Focus (Ext 1) for the Prelim course! lol

 

[nick1048]

lol I'm out of practise with ext 1 mathematics. I have to revise the entire prelim course. The only thing I remember is the trig identities, induction and applied calculus. The rest is seemingly a blur. parametrix are so hard for me, no idea y, polynomials I used to really like. goodluck to all those doing their half yearlies for 3u mathz, a.k.a me *gulp*