The polynomial of degree 3, P (x), has a root of multiplicity 2 at x = 5 and a root of multiplicity 1 at x = − 2 . The y-intercept is y = − 15 .

Question

Find a formula for P(x).



P(x)= _____.

Answer 1

x=5 is a zero with multiplicity 2

x=-2 is a zero with multiplicity 1

(x-5)^2(x+2) = (x^2-10x+25)(x+2) = x^3-8x^2+5x+50

y intercept =-15

P(x) = -(15/50)(x^3-8x^2+5x+50)

P(x) =-(3/10)(x^3-8x^2+5x+50)

P(x) = -3x^3/10 +12x^2/5 -3x/2-15

or

P(x) = -0.3x^3 +2.4x^2-1.5x -15