One zero term of f(x)=x^3-6x^2+11x-6 is 3. What are other zeros of the function?
a. 1 and 3
b. -1 and -2
c. 1 and 2
d. -1 and 3
To find the other zeros of the function, we can use synthetic division with x = 3 as the zero.
Starting with the coefficients of the function:
1 | 1 -6 11 -6
-3 -9 6
---------------
1 -9 2 0
The remainder is 0, so x = 3 is a zero of the function. Now, let's factor the resulting quadratic expression:
1x^2 - 9x + 2 = 0
We can either factor this quadratic expression or use the quadratic formula to find the other zeros. Factoring it:
(1x - 1)(1x - 2) = 0
Setting each factor equal to zero:
1x - 1 = 0 or 1x - 2 = 0
Solving for x:
x = 1 or x = 2
Therefore, the other zeros of the function are x = 1 and x = 2.
The correct answer is c. 1 and 2.