MATHEMATICS

Question

Find all rational zeros and write in factored form: f(x)=x3-3x-2

Answer 1

By the Rational Zero Theorem, the only possible rational zeros are 1, -1, 2, -2.

 

We find that -1 is a rational zero of f(x).

 

Divide f(x) synthetically by x - (-1):

 

-1⌋ 1       0      -3      -2

              -1        1       2

      1      -1      -2       0

 

f(x) = (x+1)(x² - x - 2) = (x+1)(x+1)(x-2) = (x+1)²(x-2)