Expert: Richard J. Raridon - 3/7/2005

Question
2 questions actually... :)

1. x4-x3+x-1=0
DO I factor by dividing two sect. ie (x4+x3)+...
Cannot get the right answer

2. (-sqroot of 26-11x)+4=x
Can I start by multiplying all by -1?  Tried this question about 20 times...still no luck

Answer
1. No, you factor it by finding factors. Re-write it as
f(x) = x^4-x^3+x-1
pick some value for x and calculate f(x).  If that value of x is a solution, then f(x)=0
In this case it's easy to see that x=1 is a solution so one of the factors is (x-1)
Divide that into x^4-x^3+x-1 and you get x^3+1
If you have f(x) = x^3+1 it's easy to see that x=-1 is a solution and (x+1) is a factor
Divide that into x^3+1 and you have x^2-x+1 for your third factor.  
2. -(26-11x)^1/2 = x-4
(26-11x)^1/2 = -x+4
square both sides to get
26-11x = x^2-8x+16
x^2 +3x -10 = 0 = (x+5)(x-2) so x = 2,-5