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CBSE Class 9 Polynomials and Algebraic Identities — practice questions

Explore 50 free Polynomials and Algebraic Identities questions in CBSE Class 9 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Polynomials and Algebraic Identities questions and exercises with answers

Showing questions 1–30 of 50.

Which of the following gives a LINEAR equation when set equal to zero?Read the answer and worked solution →The algebraic identity (a + b)² is equal to:Read the answer and worked solution →The identity (a − b)² is equal to:Read the answer and worked solution →The identity (a + b)(a − b) equals:Read the answer and worked solution →Use an identity to compute 102² quickly:Read the answer and worked solution →Compute 98² using an identity:Read the answer and worked solution →Compute 47 × 53 using an identity:Read the answer and worked solution →Factorise: 9x² − 25y²:Read the answer and worked solution →Find the value of x² + y² if x + y = 10 and xy = 21:Read the answer and worked solution →If a + b = 7 and a − b = 3, find a² − b²:Read the answer and worked solution →Find (x − 1/x)² if x + 1/x = 4:Read the answer and worked solution →Is (a + b)² > a² + b² always true for non-zero a, b?Read the answer and worked solution →Expand (2x + 3y)²:Read the answer and worked solution →CLASS9 · Mathematics · Polynomial DegreeRead the answer and worked solution →SAT · Mathematics · Polynomial Degree SortRead the answer and worked solution →If a, b and c are the zeros of the cubic polynomial 2x^3 - x^2 - 2x + 1, find the value of ab + bc + ca.Read the answer and worked solution →If a is positive and a² + 1/a² = 7, then a³ + 1/a³ equals:Read the answer and worked solution →Simplify: (x + 3)(x − 3).Read the answer and worked solution →Which condition must every exponent in a polynomial satisfy?Read the answer and worked solution →What is meant by the degree of a polynomial in one variable?Read the answer and worked solution →What is the first step when factorising a cubic polynomial by hand?Read the answer and worked solution →The polynomial 2x^3 minus 3x^2 plus x minus 5 is divided by x minus 2. What is the remainder?Read the answer and worked solution →The expansion of (a + b + c)2 includes which terms?Read the answer and worked solution →Which identity helps compute 119 squared quickly?Read the answer and worked solution →An identity differs from an equation because it holds for:Read the answer and worked solution →Who proposed the identity used to compute squares quickly in 750 CE?Read the answer and worked solution →Expanding (a + b + c)2 gives how many squared terms?Read the answer and worked solution →After taking out 2, the expression 25p2 + 30pq + 9q2 is the square of:Read the answer and worked solution →The highest power of the variable in a polynomial is its:Read the answer and worked solution →A polynomial of degree 2 is called:Read the answer and worked solution →

Worked practice questions

Which of the following gives a LINEAR equation when set equal to zero?

  1. x² − 4
  2. 3x + 7
  3. x³ − 1
  4. x² + 5x
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Correct answer: B. 3x + 7

A linear equation in one variable has the form ax + b = 0 (degree 1). Of the four, only 3x + 7 is a degree-1 polynomial — setting it to zero gives 3x + 7 = 0, which is a linear equation. The others have higher-degree terms and produce quadratic or cubic equations when set to zero.

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The algebraic identity (a + b)² is equal to:

  1. a² + b²
  2. a² − 2ab + b²
  3. a² + 2ab + b²
  4. a² + ab + b²
Show answer and solution

Correct answer: C. a² + 2ab + b²

**By expanding:** (a + b)² = (a + b)(a + b) = a² + ab + ba + b² = a² + 2ab + b². This holds for all real values of a and b.

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The identity (a − b)² is equal to:

  1. a² − b²
  2. a² − 2ab + b²
  3. a² + 2ab + b²
  4. a² + ab − b²
Show answer and solution

Correct answer: B. a² − 2ab + b²

We have (a − b)² = (a − b)(a − b). That is (a − b)² = a² − ab − ba + b². So (a − b)² = a² − 2ab + b². The middle term is negative, distinguishing this from (a + b)².

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