IDENTIFYING PARTS OF ALGEBRAIC EXPRESSIONS
What is factor ?
A term is the product of factors. Factors may be numerical as well as algebraic (literal).
What is algebraic expression ?
Algebraic expression is formed from variables and constants using different operations.
3x is an example of algebraic term, 4xy is also and example of algebraic term. When we combine these two terms
3x + 4xy --> Algebraic expression
Thus, expressions are made up of terms.
What is coefficient ?
Coefficient is the numerical factor in a term. Sometimes, any factor in a term is called the coefficient of the remaining part of the term.
For example,
in -2xy
The coefficient of xy is - 2.
The coefficient of -y is 2x.
Like terms and unlike terms :
The terms having the same algebraic factors are called like terms.
The terms having different algebraic factors are called unlike terms.
2x and 5x are like terms. 2x and 5xy are unlike terms.
Classifying polynomials ?
Monomial :
Expression with one term is called a monomial.
Linear :
Expression with the highest exponent 1.
Binomial :
Expression with two terms is called a binomial
Quadratic :
Expression with the highest exponent 2.
Trinomial :
Expression with three terms is called a trinomial
Cubic :
Expression with the highest exponent 3.
Identify the terms and their factors in the following expressions Show the terms and factors by tree diagrams.
Problem 1 :
x – 3
Solution :
Problem 2 :
1 + x + x2
Solution :
Problem 3 :
5xy2 + 7x2 y
Solution :
Problem 4 :
– ab + 2b2 – 3a2
Solution :
Terms are – ab, 2b2 and -3a2
Factors of -ab is -1, a and b.
Factors of 2b2 is 2, b and b.
Factors of -3a2 is -1, 3, a and a.
Problem 5 :
Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t2
(ii) 1 + t + t2 + t3
(iii) x + 2xy + 3y
Solution :
(i) 5 – 3t2
Coefficient of t2 is -3.
(ii) 1 + t + t2 + t3
Coefficient of t is 1.
Coefficient of t2 is 1.
Coefficient of t3 is 1.
(iii) x + 2xy + 3y
Coefficient of x is 1.
Coefficient of xy is 2.
Coefficient of y is 3.
Problem 6 :
Classify into monomials, binomials and trinomials.
(i) 4y – 7z
(ii) y2
(iii) x + y – xy
(iv) 100
(v) ab – a – b
Solution :
(i) 4y – 7z
Consists of 2 terms, so it is binomial.
(ii) y2
Consists of 1 term, so it is monomial.
(iii) x + y – xy
Consists of 3 terms, so it is trinomial.
(iv) 100
Consists of 1 term, so it is monomial.
(v) ab – a – b
Consists of 3 terms, so it is trinomial.
Problem 7 :
State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) –7x, 52x
(iii) – 29x, – 29y
(iv) 14xy, 42yx
(v) 4m2p, 4mp2
Solution :
(i) 1, 100 - like terms
(ii) –7x, 52x - like terms
(iii) – 29x, – 29y - unlike terms
(iv) 14xy, 42yx - like terms
(v) 4m2p, 4mp2 - unlike terms
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