1. Co-efficient, Degree and value of an algebraic expression

2. 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

3. 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

4. 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

5. 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.

6. 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

7. 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.

8. 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

9. 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

10. 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