 In the Worksheet on Types of Algebraic Expressions, you will find questions on identifying if it is monomial, binomial, trinomial, or polynomial, state if an algebraic expression is true or false or not. Practice the questions on the Types of Algebraic Expressions  Worksheet and improve your math skills and grip on the concept.

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## Types of Algebraic Expressions with Examples

I. Which of the following expressions are polynomials?
(i) 7 – 15a
(ii) 13 + 2a + 5a2
(iii) 5 + 1/x + 1/x2 + 1/x3 +1/x4
(iv) (a2 + a – 6)/(a – 2)
(v) 5 + 1/x + 1/x2 + 1/x3 +1/x4
(vi) 1/√x + 8
(vii) x + x2 + x5 – 3
(viii) 1 + 7k

Solution:

(i) Given 7-15a
Here there are two terms.
7,15a
It is a polynomial.
(ii) Given 13 + 2a + 5a2
Here there are three terms.
It is a polynomial.
(iii) Given 5 + 1/x + 1/x2 + 1/x3 +1/x4
Here there are 5 terms.
It is a polynomial.
(iv) Given (a2 + a – 6)/(a – 2)
In this example, we have variables in the denominators of the fraction.
Hence, it is not a polynomial.
(v) Given 5 + 1/x + 1/x2 + 1/x3 +1/x4
In this example, we have variables in the denominators of the fraction.
Hence, it is not a polynomial.
(vi) Given 1/√x + 8
Here there are two terms.
The first term has a square root of variables.
Hence, it is not a polynomial.
(vii) Given, x + x2 + x5 – 3
Here there are four terms.
It is a polynomial.
(viii) Given, 1 + 7k
Here there are two terms.
Hence, it is a polynomial.

II. For each expression, given below, state whether it is a monomial, binomial or trinomial:
(i) ab
(ii) xy + x
(iii) 2x ÷ y
(iv) 7xyz
(v) 7 + m + n
(vi) 2m2 – m
(vii) –x
(viii) am2 + bm – 7
(ix) -3ab + u
(x) 1 + a + b
(xi) 1 + k ÷ z
(xii) x + xy – z2

Solution:

(i) In the given expression, there is only one term.
Hence it is a monomial.
(ii) In the given expression, there are two terms.
Hence it is a binomial.
(iii) In the given expression, there is only one term.
Hence it is a monomial.
(iv)In the given expression, there is only one term.
Hence it is a monomial.
(v) In the given expression, there are three terms.
Hence it is a trinomial.
(vi) In the given expression, there are two terms.
Hence it is a binomial.
(vii) In the given expression, there is only one term.
Hence it is a monomial.
(viii) In the given expression, there are three terms.
Hence it is a trinomial
(ix) In the given expression, there are two terms.
Hence it is a binomial.
(x) In the given expression, there are three terms.
Hence it is a trinomial.
(xi) In the given expression, there are two terms.
Hence it is a binomial.
(xii) In the given expression, there are three terms.
Hence it is a trinomial.

III. Identify the following expressions, state whether they are monomials, binomials, trinomials, polynomials:
(i) 23xyz
(ii) a + 2b
(iii) x + y + z
(iv) 1 – a + a2 + a5 – a7 + a9
(v) 2mn + p
(vi) 5 + 8a + 2a3
(vii) 3ab+ 2a+ 5

Solution:

(i) In the given expression, there is only one term.
Hence it is monomial.
(ii)In the given expression, there are two terms.
Hence it is binomial.
(iii) In the given expression, there are three terms.
Hence it is trinomial.
(iv) In the given expression, there are more than three terms.
Hence it is polynomial.
(v) In the given expression, there are two terms.
Hence it is binomial.
(vi)In the given expression, there are three terms.
Hence it is trinomial.
(vii) In the given expression, there are three terms.
Hence it is trinomial.

Iv. State whether the following statements are true or false:
(i) Expression 3x2 + x is a trinomial
(ii) Expression am2 + bm + c is a trinomial
(iii) 2 × xy is a binomial
(iv) 4 + ab is a binomial
(v) x3 – 2xy + 3x + 5 is a polynomial
(vi) 7a3 + 5ab + 2a + 4 is a multinomial
(vii) 2 + 3a + 4a2 + a4 + a5 is a binomial
(viii) m2 + n2 + p2 is a trinomial

Solution:

(i) false
(ii) true
(iii) false
(iv) true
(v) true
(vi)true
(vii) false
(viii) true