Worksheet on Types of Algebraic Expressions

Practice the questions given in the worksheet on types of algebraic expressions. The questions are based on identifying whether the algebraic expressions are monomial, binomial, trinomial or polynomial.

1. State whether the following statements are true or false:

(i) Expression 5a² + a is a trinomial

(ii) Expression ax² + bx + c is a trinomial

(iii) 5 × mn is a binomial

(iv) 11 + xy is a binomial

(v) a³ – 3ab + 7a + 9 is a polynomial

(vi) 2x³ + 7xy + 3x + 2 is a multinomial

(vii) 1 + 2x + 3x² + x⁴ + x⁵ is a binomial

(viii) p² + q² + r² is a trinomial

2. Which of the following expressions are polynomials?

(i) 10 – 13x

(ii) z + z² + z⁵ - 7

(iii) 1 + 1/a + 1/a² + 1/a³ +1/a⁴

(iv) (m² + m – 2)/(m – 3)

(v) 1/2 – 5/(4 + u)

(vi) 1 + 5m

(vii) 1 + 5u + 4u²

(viii) 1/√x + 5

3. For each expression, given below, state whether it is a monomial, binomial or trinomial:

(i) mn

(ii) mn + m

(iii) 2a ÷ b

(iv) 7abc

(v) 7 + u + v

(vi) 2p² – p

(vii) –k

(viii) ax² + bx – 7

(ix) -3mn + t

(x) 1 + a + z

(xi) 1 + a ÷ z

(xii) a + ab – b²

4. Identify the following expressions are monomials, binomials, trinomials, polynomials:

(i) 11pqr

(ii) m + 2n

(iii) a + b + c

(iv) 1 – m + m² + m⁵ – m⁷ + m⁹

(v) 2ab + c

(vi) 1 + 3a + 4a³

Answers for the worksheet on types of algebraic expressions are given below to check the exact answers of the above expressions.

Answers:

1. (i) false

(ii) true

(iii) false

(iv) true

(v) true

(vi) true

(vii) false

(viii) true

2. (i) polynomial

(ii) polynomial

(iii) not polynomial

(iv) not polynomial

(v) not polynomial

(vi) polynomial

(vii) polynomial

(viii) not polynomial

3. (i) monomial

(ii) binomial

(iii) monomial

(iv) monomial

(v) trinomial

(vi) binomial

(vii) monomial

(viii) trinomial

(ix) binomial

(x) trinomial

(xi) binomial

(xii) trinomial

4. (i) monomial

(ii) binomial

(iii) trinomial

(iv) polynomial

(v) binomial

(vi) trinomial

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