SOLUTION: How do i simplify equations like f(x)= x^3 - 2x^2 + 6 or f(x)= |(x^2 -4)/(x + 3)| in other words what are some algebra tricks that i can use to simplify hard equations to find the

Algebra ->  Rational-functions -> SOLUTION: How do i simplify equations like f(x)= x^3 - 2x^2 + 6 or f(x)= |(x^2 -4)/(x + 3)| in other words what are some algebra tricks that i can use to simplify hard equations to find the       Log On


   

Question 896082: How do i simplify equations like f(x)= x^3 - 2x^2 + 6 or f(x)= |(x^2 -4)/(x + 3)| in other words what are some algebra tricks that i can use to simplify hard equations to find the x-intercepts without graphing or using a graphing calculator.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
There is no way you could have studied how to find the x-intercept of

%22f%28x%29%22=+x%5E3+-+2x%5E2+%2B+6

For only by a very advanced method the x-intercept is this irrational 
number, which can only be written in exact form as:



which by graphing calculator comes out to be approximately -1.34025083.

However for your second equation

%22f%28x%29%22=+abs%28%28x%5E2+-4%29%2F%28x+%2B+3%29%29

%22f%28x%29%22=+abs%28%28x%5E2+-4%29%29%2Fabs%28%28x+%2B+3%29%29%29

the x intercepts can be found very easily without a graphing calculator:

abs%28x%5E2+-4%29%2Fabs%28x+%2B+3%29=0 

Multiply both sides by (x+3) and the denominator disappears:

abs%28x%5E2+-4%29=0

%28x-2%29%28x%2B2%29=0

Using the zero-factor principle:

x-2=0,   x+2=0
  x=2      x=-2

So you have given an impossible one (without very advanced techniques)
and a very easy one. :)

Edwin