Question

Write a polynomial function with the given zeros.
2 = -2,1,4

Answer 1

To find a polynomial function with the given zeros, we can use the zero product property, which states that if a * b = 0, then either a = 0 or b = 0.

Therefore, the polynomial function with the specified zeros can be expressed as the product of three linear factors:

(x - (-2))(x - 1)(x - 4)

Simplifying this expression, we get:

(x + 2)(x - 1)(x - 4)

Expanding further:

(x + 2)(x^2 - 5x + 4)

Using the distributive property:

(x^2 - 5x + 4)(x) + (x^2 - 5x + 4)(2)

Multiplying each term:

x^3 - 5x^2 + 4x + 2x^2 - 10x + 8

Combining like terms:

x^3 - 3x^2 - 6x + 8

Therefore, the polynomial function with zeros -2, 1, and 4 is:

f(x) = x^3 - 3x^2 - 6x + 8