Leading term of a polynomial Example-1

1. `3x^7-6x^5`, find Leading term of a polynomial

Solution:
The Given Polynomial `=3x^7-6x^5`

The degree of a polynomial is the highest degree of its terms.

Identify the degree of each terms

The degree of term `3x^7` is `7`

The degree of term `-6x^5` is `5`

The term, that has the highest degree, gives the degree of polynomial.
`:.` Degree of polynomial `=7`

The leading term in a polynomial is the highest degree term
`:.` Leading term `=3x^7`

2. `7x-x^4`, find Leading term of a polynomial

Solution:
The Given Polynomial `=7x-x^4`

`=-x^4+7x`

The degree of a polynomial is the highest degree of its terms.

Identify the degree of each terms

The degree of term `-x^4` is `4`

The degree of term `7x` is `1`

The term, that has the highest degree, gives the degree of polynomial.
`:.` Degree of polynomial `=4`

The leading term in a polynomial is the highest degree term
`:.` Leading term `=-x^4`

3. `x^3-2x^2-x+2`, find Leading term of a polynomial

Solution:
The Given Polynomial `=x^3-2x^2-x+2`

The degree of a polynomial is the highest degree of its terms.

Identify the degree of each terms

The degree of term `x^3` is `3`

The degree of term `-2x^2` is `2`

The degree of term `-x` is `1`

The degree of term `2` is `0`

The term, that has the highest degree, gives the degree of polynomial.
`:.` Degree of polynomial `=3`

The leading term in a polynomial is the highest degree term
`:.` Leading term `=x^3`

4. `6x^3y^6+2xy+x^4`, find Leading term of a polynomial

Solution:
The Given Polynomial `=6x^3y^6+2xy+x^4`

`=x^4+6x^3y^6+2xy`

Degree of multivariate polynomial : `x^4+6x^3y^6+2xy`

For polynomials of two or more variables, the degree of a term is the sum of the exponents of the variables in the term. The degree of the polynomial is again the maximum of the degrees of all terms in the polynomial.

Identify the total degree of each terms

The degree of term `x^4` is `4`

The degree of term `6x^3y^6` is `9`

The degree of term `2xy` is `2`

The term, that has the highest degree, gives the degree of polynomial.
`:.` Degree of polynomial `=9`

The leading term in a polynomial is the highest degree term
`:.` Leading term `=6x^3y^6`

This material is intended as a summary. Use your textbook for detail explanation.
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1. Example-1