Question

A polynomial, p(x), has a lead coefficient of 1 and exactly

three distinct zeros.
• x= -2 is a zero of multiplicity of one
• x=3 is a zero of multiplicity of one
• x= -5 is a zero of multiplicity of two
Which choice show p(x)?
A) p(x) = x4 + 9x + 9x2 - 85x - 150
B) p(x) = x4 - 9x + 9x² +85x - 150
C) p(x) = x2 + 4x2 - 11x - 30
D) p(x) = x - 4x2 - 11x + 30

Answer 1

The polynomial p(x) with given zeros and multiplicities can be found by factoring.

Step-by-step explanation:

The polynomial, p(x), with a lead coefficient of 1 and exactly three distinct zeros can be found by factoring the polynomial using the given zeros and their multiplicities.

The zeros are:

• x = -2 (multiplicity of 1)
• x = 3 (multiplicity of 1)
• x = -5 (multiplicity of 2)

To find the polynomial, we can write it as:

p(x) = (x - (-2))(x - 3)(x - (-5))(x - (-5)) = (x + 2)(x - 3)(x + 5)(x + 5)

p(x) = (x + 2)(x - 3)(x + 5)2

Therefore, the correct choice is A) p(x) = x4 + 9x + 9x2 - 85x - 150.