One zero term of f(x)=x^3-6x^2+11x-6 is 3. What are other zeros of the function??

Question

a. 1 and 3
b. -1 and -2
c. 1 and 2
d. -1 and 3

Answer 1

In order to find the other zeros of the function, we need to perform polynomial division.

Dividing f(x) = x^3 - 6x^2 + 11x - 6 by x - 3:
3 │ 1 -6 11 -6
──────────────
1 -3 2 0

The remainder is 0, so x = 3 is a zero of the function.

The quotient is x^2 - 3x + 2. To find the remaining zeros, we need to solve for x when the quotient is equal to zero:

x^2 - 3x + 2 = 0

Factoring the quadratic equation:
(x - 2)(x - 1) = 0

Setting each factor equal to zero:
x - 2 = 0 or x - 1 = 0

Solving for x:
x = 2 or x = 1

Therefore, the other zeros of the function f(x) = x^3 - 6x^2 + 11x - 6 are 1 and 2.

The correct answer is c. 1 and 2.