SOLUTION: Express f(x)= x^3-7x^2+18x-13 as a polynomial in powers of (x-3). Hence,show that f(x)>0 for all x>3.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Express f(x)= x^3-7x^2+18x-13 as a polynomial in powers of (x-3). Hence,show that f(x)>0 for all x>3.      Log On


   

Question 1081690: Express f(x)= x^3-7x^2+18x-13 as a polynomial in powers of (x-3). Hence,show that f(x)>0 for all x>3.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+x%5E3-7x%5E2%2B18x-13

Let t+=+x-3

x+=+t%2B3

f%28x%29=f%28t%2B3%29=%28t%2B3%29%5E3-7%28t%2B3%29%5E2%2B18%28t%2B3%29-13%22%22=%22%22 

%28t%2B3%29%28t%2B3%29%28t%2B3%29-7%28t%2B3%29%28t%2B3%29%2B18%28t%2B3%29-13

Multiply all that out, collect like terms, and you'll get



Edwin