The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 5 and a root of multiplicity 1 at x = − 5 . The y -intercept is y = − 62.5 .

Answer 1

f(x) = k(x-5)^2(x+5)

= k(x-5)(x^2-25)

= k(x^3 - 5x^2 - 25x + 125)

f(0) = -62.5

125k = -62.5

k = -62.5/125 = -0.5

y = f(x) = -0.5 (x^3 - 5x^2 - 25x + 125)