The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=-5
Find a possible formula for P(x)
Recall that is x=a is a root, then (x-a) is a factor
P(x) = x^2 * (x-3)^2 * (x+5)
To find a possible formula for P(x), we can start by writing out the factors corresponding to each root.
Given that there are roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=-5, we can write the factors as follows:
(x - 3)^2, (x - 0)^2, (x - (-5))^1
Since the leading coefficient of P(x) is 1, the formula for P(x) can be obtained by multiplying these factors together.
P(x) = (x - 3)^2 * (x - 0)^2 * (x + 5)
Expanding this expression will give us a possible formula for P(x).