Co-efficient, Degree and value of an algebraic expression

What are coefficients? 6mn 6 * m * n 6n The coefficient of a given variable or factor in a term is another factor whose product with the given variable or factor is the term itself. Example 1:- Find Coefficient of variable m in term 6mn Solution 6mn remove m to get coefficient of m 6 * m * n Coefficient of m in 6mn is 6n

Example 2:- Find Coefficient of factor 5pq in 5pq2. Solution 5pq2 5 * p * q * q remove 5 , p , q to get coefficient of 5pq q Coefficient of 5pq in 5pq2 is

What are numerical coefficients? The numerical coefficient of a term is the number without the variables. Example1:- Numerical coefficient of 6m is 6 Example 2:- Numerical coefficient of -8r is -8 Example 3:- Numerical coefficient of 5xy is 5 Example 4:- Numerical coefficient of xy in 12xy2 – 4xy + 8 is -4

Let us consider an expression 7y2 + 5y + 3 Some more examples Identify the term which contains y and find the coefficient of y in expression 7y2+5y+3. Solution Let us consider an expression 7y2 + 5y + 3 Term 1 Term 2 Term 3 Term 2 – “5y” , contains y , and its coefficient is 5.

Power of an algebraic term Power of a term is the sum of power of all variables of a term. 3y2 Power of y =2 Power for term = 2 Powers of x = 1 Power of y = 1 Power for term=1+1=2 2xy Powers of p = 2 Power of q = 1 6p2q Power for term=2+1=3 Power for term=1 4a Power of a =1 Power for term = 0 7 No power

Degree of an algebraic expression The largest (highest) power the variable has in a polynomial with one variable. When a polynomial has more than one variable, we need to look at each term. For each term, find the degree by adding the exponents of each variable in it.

Example 1: Term 2 Term 1 Term 3 Term 4 Power of the variable is 2 Power of the variable is 4 Power of the variable is 0 (here no variable so consider as x0) Power of the variable is 1 (take x = x1) Therefore the highest power is 4, so Degree is 4

Example 2: Term 1 Term 2 Term 3 Term 4 Power of the variable is 0 (here no variable so consider as x0) Power of the variable is 3 (take x = x1) Power of the variable is 1 (take x = x1) Power of the variable is 3 Therefore the highest power is 3, so Degree is 3

Try these Find the coefficient of x in 5xy? Find the numerical coefficient of -5x2y? Identify the term that contains x and find the co-efficient of x? k2m2 + mx + 3x -8 Find the degree of the following: 4x2 - 6x +1 4yx2- 2xy + 3x + 4y