SOLUTION: Factor f(x) into linear factors given that k is a zero of f(x). f(x) = x^3 - 75x - 250; k = -5 (multiplicity 2)

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor f(x) into linear factors given that k is a zero of f(x). f(x) = x^3 - 75x - 250; k = -5 (multiplicity 2)       Log On


   

Question 1155941: Factor f(x) into linear factors given that k is a zero of f(x).
f(x) = x^3 - 75x - 250; k = -5 (multiplicity 2)
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Consider f(x) = x³ - 75x - 250 as 

f(x) = 1x³ +0x² - 75x - 250 to perform synthetic division on with -5.

-5|1  0 -75 -250
  |  -5  25  250   
   1 -5 -50    0

So we have factored

f(x) = x³ - 75x - 250

as

f(x) = (x+5)(x²-5x-50)

which factors further as

f(x) = (x+5)(x+5)(x-10)

or

f(x) = (x+5)²(x-10)

Edwin