Write a polynomial function, p(x) with degree 3 that has p(7)=0

Using the Factor Theorem, the polynomial function is given by:

The Factor Theorem states that if a function has roots , it is written as:

In which a is the leading coefficient.

In this problem:

Then:

A similar problem is given at link

is the required polynomial with degree 3 and p ( 7 ) = 0

Step-by-step explanation:

Given:

p ( 7 ) = 0

To Find:

p ( x ) = ?

Solution:

Given p ( 7 ) = 0 that means substituting 7 in the polynomial function will get the value of the polynomial as 0.

Therefore zero's of the polynomial is seven i.e 7

Degree : Highest raise to power in the polynomial is the degree of the polynomial

We have the identity,

Take a = x

        b = 7

Substitute in the identity we get

Which is the required Polynomial function in degree 3 and if we substitute 7 in the polynomial function will get the value of the polynomial function zero.

p ( 7 ) = 7³ - 21×7² + 147×7 - 7³

p ( 7 ) = 0