The polynomial of degree 5, p(x) p(x) has leading coefficient 1, has roots of multiplicity 2 at x=5 and x=0, and a root of multiplicity 1 at x=−1

find a possible formula for p(x)

Step-by-step explanation:

The given degree of the polynomial P(x)  = 5

The leading coefficient = 1

So, the general form of the polynomial  with degree 5 is

Now root x =5 is of multiplicity 2, x = 0 of multiplicity 2, x = -1 of multiplicity 1

If x = a is the zero of the polynomial of multiplicity m, then , is the factor of the polynomial.

⇒ is a factor of P(x)

is another factor of P(x)

  (x +1) is the last factor of P(x)

So, P(x) = Product of all factors =

Solving the above expression , we get

Hence,