Question

A polynomial p has zeros when x = -2, x = 1/3, and x =3.

What could be the equation of p? Choose 1 answer:
a. p(x) = (x + 2)(x + 3)(3x + 1)
b. p(x) = (x + 2)(x + 3) (3x - 1)
C. p(x) = (x + 2)(x - 3)(3x - 1)
D. p(x) = (x - 2)(x + )(3x + 1)

Answer 1

p(x) = ( x +2) (3x - 1) ( x-3)

Explanation:

We know the equation for a polynomial with given zeros is

f(x) = a(x-b1) (x-b2)...... where b are the zeros and a is a constant

Since the zeros are x = -2, x = 1/3, and x =3.

p(x) = a( x - -2) (x - 1/3) ( x-3)

p(x) = a( x +2) (x - 1/3) ( x-3)

We can pick the value of a since we are not given a point on the function. Pick a=3

p(x) = 3( x +2) (x - 1/3) ( x-3)

Rewriting the second term

p(x) = ( x +2) (3x - 1) ( x-3)