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CBSE Class 9 Maths (Term-2) Polynomials (Chapter 2) Concept, Questions and Solutions | BYJU'S

BYJU'S - Class 9 & 10・46 minutes read

The session led by Khushboo covers the basics of polynomials, including variables, constants, algebraic expressions, and classification based on the number of terms and degree. Understanding how to determine if an algebraic expression is a polynomial, finding the value of a polynomial, and identifying zeros of various types of polynomials are essential concepts discussed during the session.

Insights

  • Variables in algebraic expressions can change value, while constants remain fixed; polynomials require whole number exponents for variables and coefficients can be any real number.
  • Polynomials are categorized by the number of terms and the highest exponent of the variable present; understanding constant and zero polynomials is vital for classification and determining zeros, which are values that make the polynomial equal zero.

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Recent questions

  • What is a polynomial?

    A mathematical expression with variables and constants.

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Summary

00:00

"Introduction to Polynomials: Variables, Constants, and Exponents"

  • The session is about an introduction to polynomials, led by Khushboo.
  • Variables and constants are discussed in algebraic expressions, where variables change value and constants remain constant.
  • Variables are represented by symbols or letters, while constants are numerical values.
  • An algebraic expression is a combination of variables and constants connected by mathematical operators.
  • For an algebraic expression to be a polynomial, the exponent of the variable must be a whole number.
  • Coefficients in a polynomial can be any real number and are multiplied with variables.
  • Examples are provided to illustrate the concept of polynomials and non-polynomials.
  • Fractional or negative exponents indicate an expression is not a polynomial.
  • Practical examples are used to demonstrate the concept of polynomials.
  • Questions are posed to test understanding of polynomials in one variable, with explanations provided for each scenario.

15:35

Identifying and Classifying Polynomials in Algebra

  • A polynomial in one variable is defined by having the variable and exponents in whole numbers.
  • The presence of two variables in an expression indicates it is not a polynomial in one variable.
  • The expression x^4 + z^7 is not a polynomial in one variable due to the presence of two variables.
  • Understanding how to determine if an algebraic expression is a polynomial is crucial.
  • Terms in polynomials can be variables, constants, or a combination of both.
  • Coefficients in polynomials are the numerical values associated with variables.
  • Constant terms in polynomials are numerical values that do not change within the expression.
  • Polynomials are classified based on the number of terms as monomial, binomial, or trinomial.
  • The degree of a polynomial is determined by the highest exponent of the variable present.
  • A constant polynomial has a degree of 0 due to the absence of a variable.

29:59

Understanding Constant and Zero Polynomials in Math

  • A constant polynomial has the highest exponent of the variable as zero, making it a constant.
  • An example of a constant polynomial is 5, which remains constant even with x to the power of 0.
  • The zero polynomial has coefficients of the variable as zero, making it essential for the coefficients to be zero to classify it as such.
  • Understanding that anything raised to the power of 0 equals 1 is crucial for recognizing constant and zero polynomials.
  • The zero polynomial's coefficient of the variable must always be zero to differentiate it from other types of polynomials.
  • Classifying polynomials is based on the number of terms and the degree, with examples like binomial, trinomial, linear, quadratic, and cubic.
  • Finding the value of a polynomial involves substituting the given value for the variable and simplifying the expression.
  • Zeros of a polynomial are the values of the variable where the polynomial equals zero, such as -3 and 5 in the example provided.
  • Determining the value of a variable in a polynomial when given a zero involves substituting the zero value and solving for the unknown variable, as shown with the value of a being 11 in the given polynomial.

44:19

"Zero and Constant Polynomials Explained Simply"

  • To find the zero of a polynomial, substitute the given zero in place of the variable and equate it to 0.
  • Zeros of a zero polynomial are every real number, as the coefficient of the variable is zero, resulting in an infinite number of zeros.
  • Zeros of a constant polynomial, a non-zero constant like 5, have no zeros as any value substituted for the variable will always yield the constant value.
  • Understanding the concepts of zero and constant polynomials is crucial, with practical advice to practice questions to solidify comprehension.
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