Question

12

Which polynomial function has zeros at -3, 0, and 4?
1 f(x) = (x + 3)(x2 + 4)
2 f(x)=(x2 – 3)(x – 4)
3 F(x) = x(x + 3)(x – 4)
4 f(x) = x(x - 3)(x +4)

Answer 1

3

Explanation:

Given a polynomial with zeros x = a, x = b, x = c

Then the factors are (x - a), (x - b) and (x - c)

and the polynomial is the product of the factors

f(x) = k(x - a)(x - b)(x - c) ← k is a multiplier

here the zeros are x = - 3, x = 0, x = 4, thus the factors are

(x - (- 3)), (x - 0) and (x - 4), that is

(x + 3), x and (x - 4)

let k = 1, then

f(x) = x(x + 3)(x - 4) → 3

Answer 2

F(x) = x(x + 3)(x – 4)

Explanation:

The polynomial function has zeros at -3, 0, and 4 is F(x) = x(x + 3)(x – 4)

x(x + 3)(x – 4), set each part = 0 to find the solutions

x(x + 3)(x – 4) = 0

x = 0

x + 3 = 0; x = -3

x - 4 = 0; x = 4