Question

Write a polynomial, P(x), in factored form given the following requirements.

Degree: 3
Zeros (roots) at (−2,0) with multiplicity 2 and (3,0) with multiplicity 1
P(x) passes through the point (2,80)

Answer 1

Answer:

P(x) = - 5(x + 2)²(x - 3)

Step-by-step explanation:

Given roots x = - 2 with multiplicity 2 and x = 3 , then the factors are

(x + 2)² and (x - 3)

P(x) is then the product of the factors, that is

P(x) = a(x + 2)²(x - 3) ← a is a multiplier

To find a substitute (2, 80) into P(x)

80 = a(2 + 2)²(2 - 3) = a(16)(- 1) = - 16a ( divide both sides by - 16 )

a = - 5

P(x) = - 5(x + 2)²(x - 3)