SOLUTION: for each polynomial function: a)find the rational zeros and all the other zeroes that is solve f(x)=0. (b)express f(x) as a product of linear factors. f(x)= x^3-2x^2+16x-32 p

Algebra ->  Trigonometry-basics -> SOLUTION: for each polynomial function: a)find the rational zeros and all the other zeroes that is solve f(x)=0. (b)express f(x) as a product of linear factors. f(x)= x^3-2x^2+16x-32 p      Log On


   



Question 1138633: for each polynomial function:
a)find the rational zeros and all the other zeroes that is solve f(x)=0.
(b)express f(x) as a product of linear factors.
f(x)= x^3-2x^2+16x-32 please show your work

Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
for each polynomial function:
(a)find the rational zeros and all the other zeroes that is solve f(x)=0.
(b)express f(x) as a product of linear factors.
%22f%28x%29%22=+x%5E3-2x%5E2%2B16x-32

Factor the first two terms and the last two terms

%22f%28x%29%22=+x%5E2%28x-2%5E%22%22%29%2B16%28x-2%5E%22%22%29

Take out the common factor (x-2):

%22f%28x%29%22=+%28x-2%5E%22%22%29%28x%5E2%2B16%29%29

Write +16 as -(-16) 

%22f%28x%29%22=+%28x-2%5E%22%22%29%28x%5E2-%28-16%29%29%29

Since the square roots of -16 are 4i and -4i we can factor
x²+(-16) as the difference of squares:

%22f%28x%29%22=+%28x-2%5E%22%22%29%28x-4i%5E%22%22%29%28x%2B4i%5E%22%22%29

Set each factor = 0 to find the zeros:

x-2=0;  x-4i=0;   x+4i=0
  x=2;     x=4i;     x=-4i

Edwin


Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Here's your completed problem as I promised.

Edwin