# Evaluating an nth degree polynomial

• Mar 2nd 2013, 06:17 PM
heatly
Evaluating an nth degree polynomial
Iam having some problems understanding the question below.Does anybody know how the answers below were reached.

How many additions and multiplications are needed to evaluate an nth degree polynomial if it is evaluated:

1) by calculating each power of x and multiplying it by its coifficient. Ans: 2n-1 multiplications and n additions
2)by using the nested form of the polynomial to evaluate it. Ans: n multiplications and n additions
• Mar 2nd 2013, 06:31 PM
emakarov
Re: Evaluating an nth degree polynomial
Quote:

Originally Posted by heatly
Iam having some problems understanding the question below.
...
How many additions and multiplications are needed to evaluate an nth degree polynomial

Which word in this question don't you understand?
• Mar 2nd 2013, 06:42 PM
heatly
Re: Evaluating an nth degree polynomial
1)calculating each power of x and multiply by coeifficent.

say
f(x)=0=a0+a1x+a2x^2+......anx^n

Is'nt the powers already known.Why multiple the power by the coeifficient.Sounds like taking the derivitive of each term?
This Question is in a numerical math subject.
• Mar 2nd 2013, 06:53 PM
emakarov
Re: Evaluating an nth degree polynomial
Quote:

Originally Posted by heatly
1)calculating each power of x and multiply by coeifficent.

say
f(x)=0=a0+a1x+a2x^2+......anx^n

You are given just a polynomial f(x). I don't think you are told to assume that f(x) = 0.

Quote:

Originally Posted by heatly
Is'nt the powers already known.Why multiple the power by the coeifficient.Sounds like taking the derivitive of each term?

The question is about computing f(x) for a given number x. The first way is to calculate each term of f(x) and add them together. To compute $a_kx^k$, you compute $x^2$, $x^3$, ..., $x^k$ and finally $a_kx^k$. Note that the values of intermediate powers $x^2, x^3, ..., x^{k-1}$ can be reused to compute other terms of the polynomial.

The second way of computing f(x) is apparently Horner's method.
• Mar 2nd 2013, 09:16 PM
heatly
Re: Evaluating an nth degree polynomial
Thanks for that