Leading coefficient of a polynomial Example-1

1. `3x^7-6x^5`, find Leading coefficient 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`

The leading coefficient is the coefficient of the leading term
`:.` Leading coefficient `=3`

2. `7x-x^4`, find Leading coefficient 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`

The leading coefficient is the coefficient of the leading term
`:.` Leading coefficient `=-1`

3. `x^3-2x^2-x+2`, find Leading coefficient 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`

The leading coefficient is the coefficient of the leading term
`:.` Leading coefficient `=1`

4. `6x^3y^6+2xy+x^4`, find Leading coefficient 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`

The leading coefficient is the coefficient of the leading term
`:.` Leading coefficient `=6`

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