Problem
Question 39 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 $P(x)$. \[ P(x)= \] Question Help: $\square$ Video
Solution
Step 1 ：Given that the polynomial has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=-5, we can write the polynomial as: \(P(x) = (x-3)^2 * (x-0)^2 * (x+5)\)
Step 2 ：Expanding this expression, we get \(P(x) = x^5 - x^4 - 21x^3 + 45x^2\)
Step 3 ：\(\boxed{P(x) = x^5 - x^4 - 21x^3 + 45x^2}\) is the possible formula for the polynomial.
