Does the expression 7 x 2 y 1 2 - 5 x y represents a polynomial?

Polynomials in two variables are algebraic expressions that consist of terms in the form a x n y m where n , m are non-negative (i.e. positive or zero) integers and a is a real number and is called the coefficient of the term. In the given expression, there are 2 terms, that are 7 x 2 y 1 2 and - 5 x y . And, there is a exponent 1 2 which is not a whole number. Therefore, the given expression is not a polynomial.

Does the expression 5 x + x + 3 represents a polynomial?

Polynomials in one variable are algebraic expressions that consist of terms in the form a x n where n is a non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial. In the given expression, there are 3 terms, that are 5 x , + x and 3 but there is a term having negative power. That is 5 x = 5 x - 1 . Therefore, the given expression is not a polynomial.

Does the expression x 2 3 y - 4 x 3 y 2 3 represents a polynomial?

Polynomials in two variables are algebraic expressions that consist of terms in the form a x n y m where n , m are non-negative (i.e. positive or zero) integers and a is a real number and is called the coefficient of the term. All the exponents in the algebraic expression must be non-negative integers in order for the algebraic expression to be a polynomial. In the given expression, there are 2 terms, that are x 2 3 y and - 4 x 3 y 2 3 . And, the exponents are not integers. Therefore, the given expression is not a polynomial.

i x 2 + 7 x + 12 ii x 2 3 + x 3 iii y 3 iv 5 v 4 x 3 - x 2 + x + 3 vi 7 x 2 y 1 2 - 5 x y vii x 2 + 4 x 3 - x + 1 viii 5 x + x + 3 ix x 2 y 2 + y 2 z 2 + z 2 x 2 x x 2 3 y - 4 x 3 y 2 3 State which of the above expressions are i monomials _____ ii binomials _____ iii trinomials _____ iv other polynomials _____ v non-polynomials _____

Polynomials in one variable are algebraic expressions that consist of terms in the form a x n where n is non-negative (i.e. positive or zero) integer and a is a real number and is called the coefficient of the term. Polynomials in two variables are algebraic expressions that consist of terms in the form a x n y m where n , m are non-negative (i.e. positive or zero) integers. The three types of polynomials are: Monomial. Binomial. Trinomial. Monomials: An algebraic expression is called a monomial expression if there is only one term in the expression and there is no negative exponent for any variable in the term. iii y 3 iv 5 In above algebraic expressions, there is only 1 term. Therefore, they are monomials. Binomials: An algebraic expression is called a binomial expression if it has only two terms in the expression. There are no binomials. ii x 2 3 + x 3 vi 7 x 2 y 1 2 - 5 x y x x 2 3 y - 4 x 3 y 2 3 In above algebraic expressions, there are 2 terms. But their exponents are not integers. Therefore, they are not binomials. Trinomials: An algebraic expression in three terms is called a trinomial provided none of its terms has a negative exponent for any of the variable. i x 2 + 7 x + 12 ix x 2 y 2 + y 2 z 2 + z 2 x 2 In above algebraic expressions, there are 3 terms. Therefore, they are trinomials. Other Polynomials: Other polynomials are those polynomial which have more than three terms. v 4 x 3 - x 2 + x + 3 , vii x 2 + 4 x 3 - x + 1 , In above algebraic expressions, all the exponents are positive integers. Therefore, above expressions are other polynomials. Non-Polynomials: If any term of an expression has negative exponents, then it is not a polynomial. ii x 2 3 + x 3 , vi 7 x 2 y 1 2 - 5 x y , viii 5 x + x + 3 , x x 2 3 y - 4 x 3 y 2 3 In above algebraic expressions, there is a negative exponent, i.e. 5 x = 5 x - 1 and some exponents are not integers. Therefore, they are non-polynomials.

E M B I B E

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1

Jose Paul Solutions for Chapter: Algebraic Expressions, Exercise 1: EXERCISE 6.1

Author:Jose Paul

Jose Paul Mathematics Solutions for Exercise - Jose Paul Solutions for Chapter: Algebraic Expressions, Exercise 1: EXERCISE 6.1

Attempt the practice questions on Chapter 6: Algebraic Expressions, Exercise 1: EXERCISE 6.1 with hints and solutions to strengthen your understanding. Discovering Mathematics Book 8 solutions are prepared by Experienced Embibe Experts.

Questions from Jose Paul Solutions for Chapter: Algebraic Expressions, Exercise 1: EXERCISE 6.1 with Hints & Solutions

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does $5$ represents a polynomial?

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does the expression $4 x^{3} - x^{2} + x + 3$ represents a polynomial?

EASY

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does the expression $7 x^{2} y^{\frac{1}{2}} - 5 x y$ represents a polynomial?

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does the expression $x^{2} + 4 x^{3} - x + 1$ represents a polynomial?

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does the expression $\frac{5}{x} + x + 3$ represents a polynomial?

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does the expression $x^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2}$ represents a polynomial?

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 1

Does the expression $x^{\frac{2}{3}} y - 4 x^{3} y^{\frac{2}{3}}$ represents a polynomial?

HARD

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 6 - Algebraic Expressions>EXERCISE 6.1>Q 2

$(i) x^{2} + 7 x + 12 (ii) x^{\frac{2}{3}} + x^{3} (iii) y^{3} (iv) 5 (v) 4 x^{3} - x^{2} + x + 3 (vi) 7 x^{2} y^{\frac{1}{2}} - 5 x y (vii) x^{2} + 4 x^{3} - x + 1 (viii) \frac{5}{x} + x + 3 (ix) x^{2} y^{2} + y^{2} z^{2} + z^{2} x^{2} (x) x^{\frac{2}{3}} y - 4 x^{3} y^{\frac{2}{3}}$

State which of the above expressions are
$(i)$ monomials  _____
$(ii)$   binomials  _____
$(iii)$ trinomials  _____
$(iv)$ other polynomials _____
$(v)$ non-polynomials _____

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