The polynomial of degree 5, P ( x ) has leading coefficient a=1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 Find a possible formula for P ( x ) .

, for

Step-by-step explanation:

The general form of quintic-order polynomial is:

According to the statement of the problem, the polynomial has the following roots:

Then, some algebraic handling is done to expand the polynomial:

If , then:

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step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph