Leading Co-efficient In Polynomial

Introduction on leading coefficient:

Introduction on leading coefficient:

The leading coefficient is the coefficient which has the highest power of a term in a polynomial. A polynomial in one variable x can be written as

bkxk + . . . + b1x1 + b0,

for some integer k, where bk, ... b1, b0 are coefficients For the largest i with bi ? 0 (if any), bi is called the leading coefficient of the polynomial.

Leading Co-efficient in Polynomial:

To learn leading coefficient, we have to know the terms used in polynomial. In a polynomial, the ascending and descending order of the degree is not necessary. The given term may be of any order is the coefficient which has highest power. The terms are following below. The following examples are very helpful to learn leading coefficient. So for example the leading coefficient of the polynomial

4x5 + x3 + 2x2

Steps to find leading coefficient:

Step 1: Observe the given polynomial cleanly.

Step 2: Now take the coefficient which has the highest power in a term.

Step 3: The number which we got from step 2 is the answer.

Example Problems for Leading Co-efficient:

1) Find the leading coefficient of the term 2x3+4x2+3x-1.

Sol:

Given, the term is 2x3+4x2+3x-1.

In this the first term has a highest power.

The coefficient of the first term is 2

So, 2 is the answer.

2) Find the leading coefficient of the term 3x3+x5+-3x4+x-1.

Sol:

Given, the term is 3x3+x5+-3x 4+x-1.

In this the 2nc term has a highest power.

The coefficient of the 2nd term is 1.

So, 1 is the answer.

3) Find the leading coefficient of the term -x+2x2+x-1.

Sol:

Given, the term is -x+2x2+x-1.

In this the 2nd term has a highest power.

The coefficient of the second term is 2.

So, 2 is the answer.

4) Find the leading coefficient of the term -3x5 +2x2+-3x 4+x-1.

Sol:

Given, the term is -3x5 +x2+-3x4+x-1.

In this the first term has a highest power.

The coefficient of the first term is -3.

So, -3 is the answer.

by: jeri

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