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ICSE Class 9 Algebra: factorisation — practice questions

Explore 28 free Algebra: factorisation questions in ICSE Class 9 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra: factorisation questions and exercises with answers

Showing questions 1–28 of 28.

Factorisation expresses a polynomial as a product of what factors?Read the answer and worked solution →An irreducible polynomial cannot be factored into two what?Read the answer and worked solution →Up to sign, the content of an integer polynomial is what of coefficients?Read the answer and worked solution →An integer polynomial is primitive if the GCD of its coefficients equals:Read the answer and worked solution →Content-primitive factorisation writes an integer polynomial as a:Read the answer and worked solution →According to Gauss's lemma, the product of two primitive polynomials is:Read the answer and worked solution →A primitive polynomial is irreducible over rationals if irreducible over:Read the answer and worked solution →If two factors of a polynomial match, it is a multiple of their:Read the answer and worked solution →Any multiple factor of a polynomial must also be a factor of its:Read the answer and worked solution →Which test finds all rational linear factors of an integer polynomial?Read the answer and worked solution →Factoring a reducible cubic completely yields three linear factors or:Read the answer and worked solution →Kronecker's polynomial factorisation method relies on evaluation at:Read the answer and worked solution →A polynomial GCD of two polynomials is a common factor polynomial of:Read the answer and worked solution →Every common divisor of two polynomials p and q must also divide their:Read the answer and worked solution →A greatest common divisor of two polynomials is unique up to what factor?Read the answer and worked solution →Over a field, the standard univariate polynomial GCD is chosen to be:Read the answer and worked solution →Two polynomials whose only common divisors are constants are called:Read the answer and worked solution →For any polynomial r, gcd(p, q) equals which equivalent GCD expression?Read the answer and worked solution →Expressing gcd(p, q) as a combination ap + bq is named after:Read the answer and worked solution →Finding polynomial GCD by complete factorisation takes the product of:Read the answer and worked solution →What is the greatest common divisor of x^2 + 7x + 6 and x^2 - 5x - 6?Read the answer and worked solution →In Euclid's algorithm for polynomials, what strictly decreases each step?Read the answer and worked solution →In the Euclidean algorithm, the polynomial GCD is obtained from the:Read the answer and worked solution →Multiple roots of a polynomial are roots of the GCD of itself and its:Read the answer and worked solution →Match each sum or difference of cubes with its factored binomial-trinomial form:Read the answer and worked solution →Match each polynomial with its complete factorisation:Read the answer and worked solution →Match each quadratic trinomial with its factored binomials:Read the answer and worked solution →Match each algebraic theorem with its mathematical statement:Read the answer and worked solution →

Worked practice questions

Factorisation expresses a polynomial as a product of what factors?

  1. Irreducible factors
  2. Reciprocal factors
  3. Imaginary factors
  4. Fractional factors
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Correct answer: A. Irreducible factors

Polynomial factorisation writes an expression as a product of irreducible factors.

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An irreducible polynomial cannot be factored into two what?

  1. Monic polynomials
  2. Linear expressions
  3. Non-constant factors
  4. Rational monomials
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Correct answer: C. Non-constant factors

Irreducible polynomials cannot be factored into two non-constant polynomials.

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Up to sign, the content of an integer polynomial is what of coefficients?

  1. Sum of coefficients
  2. GCD of coefficients
  3. Product of values
  4. Leading coefficient
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Correct answer: B. GCD of coefficients

The content of an integer polynomial is the greatest common divisor of its coefficients.

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