Answer: p(x) = a (x-b)(x-c)(x-d)
Step-by-step explanation:
The first step is to determine the degree of the polynomial.
It shall depend totally on the linear factors given for the polynomial.
If there is one, it is a linear polynomial.
If there are 2, then it is a quadratic polynomial.
If there are three then it shall be a cubic polynomial.
Now let us assume that there are three linear factors.
We multiply those factors and write the polynomial.
If x-b, x-c & x-d are the factors we write
p(x) = (x-b)(x-c)(x-d)
But as we may have a leading coefficient so we write the polynomial as
Then we go on to expand this to get the polynomial in the standard form.
Answer with Step-by-step explanation:
First we find the degree of polynomial.
Consider two linear factors
(x-a) and (x-b)
Multiplying these two factors to get the polynomial.
[tex]p(x)=(x-a)(x-b)=x^2-(a+b)x+ab[/tex]
There are two linear factors .
Therefore, the degree of polynomial is 2 and the polynomial is quadratic.
Degree of polynomial=Number of linear factors
If the linear factors are three then the polynomial formed by multiplying theses factors .
Then, we get the polynomial of degree 3 and the polynomial is cubic polynomial.
It we have four linear factors.
After multiplying these four factors, we get a polynomial of degree 4.
The polynomial is bi quadratic.
