Ex.9.1 Q2 Algebraic Expressions and Identities - NCERT Maths Class 8

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Question

Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories?

\(\begin{align}&x + y,\\ &1000,\\ & x + {x^2} + {x^3} + {x^4},\\ & 7 + y + 5x,\\ & 2y - 3{y^2},\\ & 2y - 3{y^2} + 4{y^3},\\ &5x - 4y + 3xy,\\ & 4z - 15{z^2},\\ &  ab + bc + cd + da,\\ & pqr,\\ & {p^2}q + p{q^2},\\ & 2p + 2q\end{align}\)

Text Solution

What is known?

Expression

What is unknown?

The degree of the expression.

Reasoning:

1. Expression that contains only one term is called a monomial.

2. Expression that contains two terms is called a binomial.

3. Expression containing three terms is a trinomial and so on.

4. An expression containing, one or more terms with non-zero coefficient (with variables having non-negative integers as exponents) is called a polynomial.

5. A polynomial may contain any number of terms, one or more than one.

Steps:

The given expressions are classified as

Monomials: \(1000,\; pqr\)

Binomials:

\[\begin{align} &x + y,\;2y - 3{y^2},\\ & 4z - 15{z^2},\\ & {p^2}q + p{q^2},\\ & 2p + 2q \end{align}\]

Trinomials:

\[\begin{align} &7 + y + 5x,\\ & 2y - 3{y^2} + 4{y^3},\\ & 5x - 4y + 3xy \end{align} \]

Polynomials that do not fit in any of these categories are

\[\begin{align} x + {x^2} + {x^3} + {x^4},\\ab + bc + cd + da \end{align} \]

  
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