Question

The polynomial P(x) = 3 – 2x2 + 5x5 – 7x7 has what order?

Answer 1

This, polynomial has order 7.

Explanation:

Given the polynomial

P(x) = 3 – 2x2 + 5x5 – 7x7

`P(x) = 3 - 2x^2+ 5x^5 - 7x^7`

Order for any polynomial is highest exponential value for variables . The exponent for polynomial is also called as degree.

Hence in terms of degree, the term in polynomial which has the highest degree . That degree is the order of the polynomial.

For example ,

in
`x^5 + x^8 + x^9`

here we see that variable x has highest power of 9. Thus, order of the given equation is 9.

Similarly for the polynomial given we see that

in the polynomial
`P(x) = 3 - 2x^2+ 5x^5 - 7x^7`

x has three power 2, 5 and 7 .

As 7 is the highest power of P(x) = 3 - 2x^2+ 5x^5 - 7x^7

This, polynomial has order 7.