Question

O f(x) = (x + 1)(x-2)(x - 3)

Of(x) = (x - 1)(x + 2)(x+3)
Of(x) = (x + 1)(x + 2)(x+3)
Of(x) = (x - 1)(x - 2)(x − 3)

Answer 1

D) f(x) = (x - 1)(x - 2)(x - 3)

Explanation:

From inspection of the given graph, the points at which the curve intersects the x-axis are:

• (1, 0)
• (2, 0)
• (3, 0)

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

According to the factor theorem, as f(x) = 0 when x = 1, x = 2 and x = 3 then (x - 1) and (x - 2) and (x - 3) are factors of the polynomial.

Therefore, the equation of the function is:

• f(x) = (x - 1)(x - 2)(x - 3)

Answer 2

• D) f(x) = (x - 1)(x - 2)(x - 3)

-------------------------------------

The x-intercepts are the roots of the function and according to the graph the roots are:

• 1, 2 and 3

Hence the function is:

• f(x) = (x - 1)(x - 2)(x - 3)