Important Questions with Solutions for CBSE Class 9 Maths Chapter 2 - Polynomials

It is the most extensively used subject in science and computer, standing based on logic and reasoning. Therefore, every student must have an in-depth learning of the subject to frame a successful career. Students with a weak core of knowledge in Mathematics may face difficulties to deal with the complex formulas and concepts of Maths, which in return serves as a hurdle to score well in the examination. In class 9, algebra is one of the crucial domains of Maths where maximum students fumble.

An efficient learning algebra and its concepts enable the students to dismantle diplomatic Mathematics problems into more straightforward and convenient processes. Therefordents must practice important questions for class 9  maths chapter 2 to master the topic perfectly. Students who find the topic challenging or get stuck with any concept or problems of algebra many refer to the detailed solutions available on the Internet. Quality study material like important questions for class 9 maths polynomials are also availed for the students to access freely in text and PDF formats.

Class 9 Maths Chapter 2 Important Questions

Students are presented with an extensive view of the algebraic concepts and theories in class 9 Maths Ch 2 important questions. To explore different concepts of the chapter and practice a variety of problems, students must have their hands on important polynomials for class 9. Now, let's discuss some of the details about the chapter:

Polynomials

Polynomials can be quoted as an algebraic expression formed using indeterminates or variables and constants or coefficients. This algebraic expression allows such to perform addition, subtraction, multiplication, positive integer exponentiation of variables. The word polynomial is framed from 'poly' meaning 'many' and 'nominal' meaning 'term,' depicting many terms, which means a polynomial contains many terms but not infinite terms.

A polynomial expression comprises variables like x, y,z, coefficients like 1,2, and exponents like 2 in x². The polynomial function is generally depicted by P(x), where x is the variable. For instance,

P(x) = x² + 7x + 15, here x is the variable and 15 is the constant.

Types of Polynomials

Polynomials are categorised into three groups depending upon the number of terms it comprises of. Here are the types of polynomials.

Monomial

A monomial is a type of polynomial in algebra consisting of a single non-zero term. A polynomial expression consists of one or more terms. Therefore, every term of a polynomial expression is a monomial. Every numeric value such as 6, 12, 151 is a monomial by itself, whereas the variables can x, y, a can also be included in the list of monomials in algebra. Example of a monomial expression – 7x².

Rules for monomial algebraic expressions:

If a monomial is multiplied by a constant, the output will also be a monomial.

If a monomial is multiplied by a monomial, the result will also be a monomial. For instance, if a monomial three is multiplied by 3, the result 8 is also a monomial.

Binomial

A binomial is a type of polynomial expression comprising of two non-zero terms. Let's see some examples to make it clear,

7x² + 8y is a binomial expression with two variables.

10x⁴ + 9y is also a binomial expression with two variables.

Trinomial

A trinomial is a type of polynomial expression comprising of three non-zero terms. Let's see some examples to make it clear,

5x²+8x+9 is a trinomial expression with one variables x.

a + b+ c is a trinomial expression with three variables.

7x – 6y + 9z is a trinomial expression with three variables.

Students can explore different questions polynomial types through the class 9 Maths chapter 2 important questions.

Polynomial Theorems

Some of the vital theorems of polynomials are as follows:

Remainder Theorem

The polynomial remainder theorem, also quoted as the little Bezout's theorem, implies that if a polynomial P(x) is divided by any linear polynomial depicted by (x – a), the remainder of the operation will be a constant given by P(a), i.e., r = P(a).

Factor Theorem

The factor theorem implies that if P(x) is a polynomial of degree n > 1, and 'a' is a real number, this portrays that:

If P(x) = 0, then (x – a) is the factor of P(x),

If (x – a) is the factor of P(x), P(x) = 0.

Bezout's Theorem

Bezout's Theorem states that if P(x) = 0, then P(x) gets divided by (x – a), with 'r' as the remainder.

Intermediate Value Theorem

The intermediate value theorem states that when a polynomial function transforms from a negative to a positive value, it must cross the x-axis. In other words, the theorem highlights the properties of continuity of a function.

Fundamental Theorem of Algebra

The fundamental theorem of algebra states that each non-constant single variable that consists of a complex coefficient possess a minimum of one complex root.

Polynomial Equations

A polynomial equation is an algebraic equation comprising of variables with positive integer exponents and constants. A polynomial expression may contain many exponents, and the highest exponent value is termed as the degree of the equation. Let's take an example to make it clear,

ax⁴ + bx² + x + c, is a polynomial expression with degree = 4.

Algebraic identities of polynomials

Identity 1 : (x + z )2 = x² + 2xz + z²

Identity 2 : (y – z) 2 = y² – 2yz + z²

Identity 3 : y² – z² = (y + z) (y – z)

Identity 4 : (x + y) (x + z) = x² + (y + z)x + yz

Important Questions of Polynomials for Class 9

To present the students an insight into the algebraic world, we have highlighted here some of the important questions class 9 Maths chapter 2, after a proper analysis of sample question papers:

• What is a polynomial? Explain with example.

• What are the types of polynomial expressions?

• Explain the Remainder Theorem with an example.

• Prove the Factor theorem of polynomials.

• Illustrate Bezout's Theorem, and mention it's importance.

• What do you mean by the degree of the polynomial? Explain with examples.

• How can we add or subtract polynomials?

• Explain the standard form of polynomials.

• What do you mean by roots of equations? And how to find them.

• Find the roots of polynomial equation, f(x) = x⁴ + 5x² + 7x + 19.

Benefits of Class 9 Maths Ch 2 Important Questions

The students preparing for the boards in the upcoming year must prepare a strong core foundation for developing an in-depth logic and understanding of algebra. Therefore they can blend the benefits by practising the class 9th Maths chapter 2 important questions. Here we have listed some of the fruitfulness of class 9 polynomials important questions:

• Students can develop deep learning of the topics by exploring different types of questions presented in the important polynomials for class 9.

• Vedantu, with an efficient team of top-notch educators, has carefully designed the questions after proper research and analysis of the past year's question papers and sample test papers.

• The important questions of ch 2 Maths class 9 are carefully designed under the CBSE board's rules’ strict guidance.

• To perform well in mathematics, academic success is practice; the students must efficiently practice the polynomials class 9 important questions.

• To prevent any issues or mistakes in the important questions for class 9 maths polynomials, expert teachers have reviewed and analysed the papers.

Conclusion

Mathematics is the foundation for logic and reasoning. As a result, in order to grasp the topic's various subjects, students must work with insufficient fundamental Mathematics comprehension and study important polynomial questions for class 9. Students must have a good comprehension of the crucial questions for class 9 mathematics chapter 2 in order to begin a career in science and technology.

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