Find the equation for the polynomial function with the following information: degree 3
zero at 1 with multiplicity 1, zero at 2 with multiplicity 1, and zero at -1 with multiplicity 3.
y-intercept at 2

y = x⁵ - 4x³ - 2x² + 3x + 2

Step-by-step explanation:

There is a major disconnect in your question.

The sum of your multiplicities must equal the degree of the polynomial.

IF

we ASSUME that the multiplicity sum is correct and the polynomial degree is not 3 but 5

THEN

y = (x - 1)(x - 2)(x + 1)(x + 1)(x + 1)

y = (x - 1)(x - 2)(x + 1)(x² + 2x + 1)

y = (x - 1)(x - 2)(x³ + 3x² + 3x + 1)

y = (x - 1)(x⁴ + x³ - 3x² - 5x - 2)

y = x⁵ - 4x³ - 2x² + 3x + 2

A quick plot shows that our zeros and y intercept are correct and the curve shapes at the zeros display the correct characteristics for the multiplicities.

2500

step-by-step explanation: