Use complete sentenced to explain how to use linear factors to determine teh equation of a polynomial function

Suppose a Polynomial function is

Let roots of the Polynomial Function which is cubic,so it will have three roots.

x=p,q,r

x-p=0-------(1)

x-q=0--------(2)

x-r=0---------(3)

So, in terms of linear factors the above cubic function can be written as, As it is cubic function , the linear expressions must be multiplied with each other.

Multiplying equation (1) ,(2) and (3), we get

 =(x-p)(x-q)(x-r)

When multiplied together, results in a cubic equation .

This can be explained in another way also.

If an equation has one root, it means one linear factor, so it is a Linear Polynomial.

If an equation has two root, it means two linear factor, so it is a Quadratic Polynomial.

If an equation has three roots, it means three linear factors, so it is a cubic Polynomial.

Four roots, Fourth Degree Polynomial.

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