Question

If p = 9 then find the degree of the polynomial:
f(x)= (x-p) ^3 + 729
Please answer

Regards

Answer 1

Here degree of this polynomial is 3
since The degree of a polynomial is the highest power of x with non zero coefficient.

f(x)=(x-p)3+729
= x^3-p^3-(3*x*p(x-p)) +729 {since (a − b)3 = a3 − b3 − 3ab(a − b)}
=x^3-729-(3*x*9(x-9)) {since given p=9
=x^3-729-27x^2+243x
Rearranging we will get
p(x)=x^3 - 27x^2 +243x -729
Highest ie,degree highest power of x (with nonzero coefficient)is 3.So degree of this polynomial is 3