Polynomial Functions

Question

The polynomial of degree , , has a root of multiplicity  at  and a root of multiplicity  at . The -intercept is .

Answer 1

First, a root of multiplicity 2 at x=1:

(x-1)²=0

a root of multiplicity 1 at x=−4:

x+4=0

Polynomial function of degree 3:

P(x)= a (x-1)² (x+4)

Y-intercept of -0.8 (here, x=0):

P(0) = -0.8 = a (0-1)² (0+4)

-0.8 = 4a

a =-0.2

Therefore the polynomial function of degree 3 in factored form is:

P(x) = -0.2 (x-1)² (x+4)

In standard form is:

P(x)= -0.2x³ -0.4x² + 1.4x -0.8

Answer 2

P(x) = a(x - 1)²(x + 4)

-0.8 = a(0 - 1)²(0 + 4)

Can you solve for a and answer?