The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at

Question

x=0 and x=−2. It goes through the point (5,84).

Find a formula for P(x).

P(x) =____________

Answer 1

Just in factored form, you get x(x+2)(x-3)(x-3) which expands out to

X^4 - 4x^3 - 3x^2 + 18x

but you must add on a certain integer to satisfy the above condition that it goes through the point (5,84) so

84 = 5^4 - 4 * 5^3 - 3 * 5^2 + 18*5 + c (some arbitrary constant)

using algebra

84 = 140 + c

c = - 56

P(x) = x^4 - 4x^3 - 3x^2 + 18x - 56