Class 9 Maths Polynomials MCQs with Answer

Class 9 Maths Polynomials MCQs

Understanding polynomials is very important for students of Class 9 because this chapter builds the foundation for algebra and higher mathematics concepts. This section on Class 9 Maths Polynomials MCQs with Answer is designed to help students practice important concepts in an easy and understandable way. These questions follow the latest syllabus of the CBSE Board and are useful for school exams, unit tests, and competitive exam preparation.

The polynomials class 9 mcq set includes questions on polynomial expressions, terms, coefficients, variables, constants, and zeroes of polynomials. Students can also practice class 9 maths chapter 2 mcq with answers to improve conceptual clarity and strengthen problem-solving skills. Regular practice of polynomial mcq class 9 helps students avoid common mistakes and understand algebraic expressions more confidently.

In addition, students can attempt a class 9 maths chapter 2 mcq online test to improve their speed and accuracy. These MCQs are based on concepts like identifying types of polynomials, finding zeroes, understanding algebraic identities, and evaluating polynomial expressions. Many students find this chapter slightly confusing at first because of algebraic terms and expressions, but with proper practice, the concepts become much easier to understand.

What is Polynomial MCQ Class 9?

Polynomial MCQs for Class 9 Maths are multiple-choice questions that test a student’s understanding of polynomial expressions and related concepts. These questions are an important part of Class 9 Maths Chapter 2 MCQs with answers and help students prepare effectively for exams.

In these questions, students learn about terms, variables, coefficients, constants, monomials, binomials, trinomials, and zeroes of polynomials. Students also practice identifying polynomial degrees and solving algebraic expressions.

Regular practice of polynomial mcq class 9 improves conceptual understanding, calculation speed, and confidence. It also helps students score better in CBSE Board exams and online tests.

Types of Polynomials in Maths

This table is very helpful for solving class 9 maths chapter 2 mcq online test questions quickly.

Important Tricks for Polynomial MCQs (Class 9)

Here are some simple tricks used in polynomials class 9 mcq questions:

Identify Degree Carefully:
The highest power of the variable is called the degree of the polynomial.

Check Number of Terms:
One term = Monomial, Two terms = Binomial, Three terms = Trinomial.

Finding Zeroes:
Put the polynomial equal to zero and solve for the variable.

Understand Coefficients:
The numerical value attached to a variable is called its coefficient.

These tricks are very useful in solving class 9 maths polynomials MCQs with answers.

Q. Which of the following statements is true regarding the classification of polynomials based on the number of terms?

1. A polynomial with two terms is always a monomial.
2. A trinomial must have a degree of 3.
3. A monomial has exactly one term.
4. A binomial can have any number of terms greater than one.

Answer: C

Explanation:

By definition, a monomial is an algebraic expression consisting of a single term. A polynomial with two terms is a binomial, and a trinomial has three terms. The degree of a polynomial is independent of the number of terms.

Q. Identify the degree of the polynomial: 5x3y2 - 3x4 + 7y5 - 2.

1. 3
2. 4
3. 5
4. 7

Answer: C

Explaination:

The degree of a polynomial is the highest degree of its terms. For 5x3y2, the degree is 3+2=5. For -3x4, the degree is 4. For 7y5, the degree is 5. The constant term -2 has a degree of 0. The highest degree among these is 5.

Q. Which of the following expressions is NOT a polynomial?

1. x2 + 2x - 1
2. √x + 3
3. y3 - 5y2 + 1/2
4. 7z4

Answer: B

Explaination:

A polynomial must have non-negative integer powers for its variables. In √x + 3, the term √x can be written as x1/2, which has a fractional power. Therefore, it is not a polynomial.

Q. If p(x) = 2x3 - x2 + 5, what is the value of p(-1)?

1. 2
2. -2
3. 6
4. 8

Answer: B

Explaination:

To find p(-1), substitute x = -1 into the polynomial: p(-1) = 2(-1)3 - (-1)2 + 5 = 2(-1) - (1) + 5 = -2 - 1 + 5 = 2.

Q. Which of the following is a constant polynomial?

1. 2x + 1
2. x2 - 3
3. 5
4. x3

Answer: C

Explaination:

A constant polynomial is a polynomial that consists only of a constant term. Its degree is 0. Among the options, '5' is a constant polynomial.

Q. If a polynomial p(x) has a zero at x = 'a', what does this imply about the graph of p(x)?

1. The graph of p(x) intersects the y-axis at 'a'.
2. The graph of p(x) intersects the x-axis at 'a'.
3. The graph of p(x) has a maximum point at x = 'a'.
4. The graph of p(x) has a minimum point at x = 'a'.

Answer: B

Explaination:

A zero of a polynomial p(x) is a value 'a' for which p(a) = 0. On a graph, this means that the point (a, 0) is on the graph, which is an x-intercept. Therefore, the graph intersects the x-axis at 'a'.

Q. Consider the polynomial p(x) = x2 - 4. Which of the following values are zeroes of p(x)?

1. 2 only
2. -2 only
3. 2 and -2
4. 0

Answer: C

Explaination:

To find the zeroes, set p(x) = 0: x2 - 4 = 0. This implies x2 = 4, so x = √4 or x = -√4. Thus, x = 2 or x = -2. Both 2 and -2 are zeroes of the polynomial.

Q. A polynomial of degree 1 is called a:

1. Quadratic polynomial
2. Linear polynomial
3. Cubic polynomial
4. Constant polynomial

Answer: B

Explaination:

Polynomials are classified by their degree. A polynomial of degree 1 is a linear polynomial (e.g., ax + b). A degree 2 is quadratic, degree 3 is cubic, and degree 0 is constant.

Q. Which of the following represents a polynomial in one variable?

1. x2 + y2
2. 3x-1 + 2
3. √2x + 5
4. 1/x + 4

Answer: C

Explaination:

A polynomial in one variable must have only one type of variable, and all powers of that variable must be non-negative integers. Option 1 has two variables (x, y). Option 2 has a negative power (x-1). Option 4 has a variable in the denominator (1/x = x-1). Option 3, √2x + 5, can be written as (√2)x + 5, which is a linear polynomial in one variable 'x' with a non-negative integer power (1).

Q. For a polynomial p(x), if p(k) = 0, then (x-k) is a factor of p(x). This is known as the:

1. Remainder Theorem
2. Factor Theorem
3. Fundamental Theorem of Algebra
4. Binomial Theorem

Answer: B

Explaination:

The Factor Theorem states that if p(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then (x-a) is a factor of p(x) if and only if p(a) = 0.

Q. Which of the following is a quadratic polynomial?

1. 3x + 5
2. x3 - 2x + 1
3. 2x2 - 4x + 7
4. 4

Answer: C

Explaination:

A quadratic polynomial is a polynomial of degree 2. The expression 2x2 - 4x + 7 has the highest power of x as 2, making it a quadratic polynomial.

Q. What is the coefficient of x in the polynomial 7x3 - 5x2 + x - 9?

1. 7
2. -5
3. 1
4. -9

Answer: C

Explaination:

The coefficient of a term is the numerical factor multiplying the variable(s). In the term 'x', the coefficient is 1 (since x = 1*x).

Q. If p(x) = x - 5, what is the zero of the polynomial?

1. -5
2. 0
3. 5
4. 1

Answer: C

Explaination:

To find the zero, set p(x) = 0: x - 5 = 0. Solving for x gives x = 5. So, 5 is the zero of the polynomial.

Q. Which statement accurately describes the difference between a variable and a constant in algebraic expressions?

1. A variable has a fixed numerical value, while a constant can change.
2. A variable is represented by a letter and its value can change, while a constant is a fixed numerical value.
3. Both variables and constants are always represented by letters.
4. A constant is always 0, and a variable is always 1.

Answer: B

Explaination:

In algebra, variables (like x, y, z) are symbols that can represent different values, whereas constants (like 5, -2, π) are fixed numerical values that do not change.

Q. If p(x) = ax + b, and p(0) = 3 and p(1) = 5, find the values of 'a' and 'b'.

1. a=3, b=2
2. a=2, b=3
3. a=5, b=3
4. a=-2, b=3 

Answer: B

Explaination:

Given p(x) = ax + b. From p(0) = 3: a(0) + b = 3 => b = 3. From p(1) = 5: a(1) + b = 5 => a + b = 5. Substitute b=3 into the second equation: a + 3 = 5 => a = 2. So, a=2 and b=3.

Q. The number of zeroes a cubic polynomial can have is:

1. Exactly 1
2. Exactly 2
3. At most 3
4. Any number

Answer: C

Explaination:

For any polynomial, the number of zeroes (real or complex) is equal to its degree. For a cubic polynomial (degree 3), there can be at most 3 real zeroes. It can also have fewer real zeroes if some are complex or repeated.

Q. What is the primary characteristic that differentiates a polynomial from other algebraic expressions?

1. It must contain at least three terms.
2. All variable powers must be positive integers.
3. It must have a constant term.
4. Its variables cannot appear in the denominator.

Answer: B

Explanation:

For an expression to be a polynomial, the powers of its variables must be non-negative integers (0, 1, 2, ...). This implies that variables cannot have negative powers (like x-1 or 1/x) or fractional powers (like x1/2 or √x). Therefore, options 2 and 4 (which implies no negative powers for variables) are both correct characteristics.

Q. A polynomial with two terms is called a:

1. Monomial
2. Binomial
3. Trinomial
4. Quadrinomial

Answer: B

Explaination:

The classification of polynomials by the number of terms states: one term is a monomial, two terms is a binomial, and three terms is a trinomial.

Q. What is the degree of the polynomial 8?

1. 1
2. 8
3. 0
4. Undefined

Answer: C

Explaination:

A non-zero constant, like 8, is considered a constant polynomial. The degree of a non-zero constant polynomial is 0, because it can be written as 8x0.

Q. If p(x) = x3 - 3x2 + 2x, then p(2) is:

1. 0
2. 2
3. 4
4. 8

Answer: A

Explaiantion:

Substitute x = 2 into the polynomial: p(2) = (2)3 - 3(2)2 + 2(2) = 8 - 3(4) + 4 = 8 - 12 + 4 = 0.

Q. Which of the following is NOT a characteristic of a polynomial term?

1. It can be a constant.
2. It can have variables with negative exponents.
3. It consists of a coefficient and one or more variables raised to non-negative integer powers.
4. It can be a product of a constant and variables.

Answer: B

Explaination:

A fundamental rule for polynomials is that the exponents of the variables must be non-negative integers. Therefore, terms with negative exponents (e.g., x-2) are not part of a polynomial.

Q. The graph of a linear polynomial y = ax + b (where a ≠ 0) is always a:

1. Parabola
2. Straight line
3. Curve
4. Point

Answer: B

Explaination:

A linear polynomial is defined by its degree being 1. The graph of any equation of the form y = mx + c (or y = ax + b) is a straight line, where 'm' (or 'a') is the slope and 'c' (or 'b') is the y-intercept.

Q. If p(x) = x2 - 2x + 1, which of the following is true?

1. p(0) = 0
2. p(1) = 0
3. p(2) = 0
4. p(-1) = 0

Answer: B

Explaination:

Let's check each option: p(0) = (0)2 - 2(0) + 1 = 1 ≠ 0 p(1) = (1)2 - 2(1) + 1 = 1 - 2 + 1 = 0 p(2) = (2)2 - 2(2) + 1 = 4 - 4 + 1 = 1 ≠ 0 p(-1) = (-1)2 - 2(-1) + 1 = 1 + 2 + 1 = 4 ≠ 0 So, p(1) = 0 is true.

Q. The expression 1/x2 + 3x - 5 is not a polynomial because: 

1. It has a constant term.
2. It has a term with a negative exponent.
3. It has three terms.
4. The coefficients are not integers.

Answer: B

Explaination:

The term 1/x2 can be written as x-2. For an expression to be a polynomial, all variable exponents must be non-negative integers. A negative exponent disqualifies it from being a polynomial.

Q. How many terms are in the polynomial 3x4 - 2x3 + 5x - 7?

1. 3
2. 4
3. 5
4. 7

Answer: B

Explaination:

Terms in a polynomial are separated by addition or subtraction signs. In 3x4 - 2x3 + 5x - 7, the terms are 3x4, -2x3, 5x, and -7. There are 4 terms.

Q. If the graph of a polynomial touches the x-axis at a point and does not cross it, what does this indicate about the zero at that point?

1. It is a simple zero (multiplicity 1).
2. It is a zero with even multiplicity (e.g., 2, 4).
3. It is a zero with odd multiplicity (e.g., 3, 5).
4. It is not a real zero.

Answer: D

Explaiantion:

When a polynomial's graph touches the x-axis at an x-intercept but does not cross it, it means that the corresponding zero has an even multiplicity. For example, in y = (x-a)2, the graph touches the x-axis at x=a and turns around.

Q. Which of the following is an example of a cubic polynomial?

1. x2 + 2x - 3
2. 4x - 1
3. x3 + 5x2 - 2x + 10
4. 7

Answer: C

Explaination:

x3 + 5x2 - 2x + 10 

Q. If p(x) = (x-1)(x+2)(x-3), what are the zeroes of the polynomial? 

1. 1, 2, 3
2. 1, -2, 3
3. -1, 2, -3
4. -1, -2, -3

Answer: B

Explanation:

To find the zeroes, set each factor to zero: x-1 = 0 => x = 1 x+2 = 0 => x = -2 x-3 = 0 => x = 3 The zeroes are 1, -2, and 3.

Q. Which property is essential for an algebraic expression to be classified as a polynomial?

1. It must have at least one variable.
2. All exponents of variables must be rational numbers.
3. The variables must not be under a radical sign or in the denominator.
4. Its degree must be greater than zero. 

Answer: C

Explaination:

For an expression to be a polynomial, the powers of its variables must be non-negative integers. This specifically excludes variables appearing under a radical sign (which implies fractional powers) or in the denominator (which implies negative powers). Option 2 is incorrect as exponents must be non-negative integers, a subset of rational numbers. Option 1 is incorrect as constant polynomials exist. Option 4 is incorrect as constant polynomials have degree zero.

Q. If p(x) = 2x - 6, what is the value of x for which p(x) = 0?

1. -3
2. 0
3. 3
4. 6

Answer: C

Explaination:

Set p(x) = 0: 2x - 6 = 0. Add 6 to both sides: 2x = 6. Divide by 2: x = 3. So, the value of x for which p(x) = 0 is 3.

Polynomials MCQ Preparation Tips

Follow these simple tips to score better:

Learn the definitions of terms, coefficients, and variables properly

Practice identifying the degree of different polynomials

Solve algebraic expressions step by step carefully

Revise algebraic identities regularly

Attempt polynomial mcq class 9 online tests for better practice

Use NCERT and CBSE-based study material for preparation

Conclusion

Practicing Class 9 Maths Polynomials MCQs with answers is one of the best ways to strengthen algebra concepts and improve problem-solving skills. It helps students prepare effectively for school exams, online tests, and future mathematics topics.

Regular practice also increases confidence and reduces confusion while solving algebraic expressions and polynomial-based questions.