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NSC / Matric Polynomials — practice questions

Explore 4 free Polynomials questions in NSC / Matric Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Polynomials questions and exercises with answers

Showing questions 1–4 of 4.

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 →

Worked practice questions

Which condition must every exponent in a polynomial satisfy?

  1. It must be a negative number
  2. It must be a fraction below one
  3. It must be an irrational number
  4. It must be a natural number
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Correct answer: D. It must be a natural number

1. A polynomial is built from variables raised to powers, with coefficients in front of them. 2. The definition allows only exponents drawn from the natural numbers. 3. An expression with a square root or a negative exponent is therefore not a polynomial. 4. Checking the exponents is the quickest way to test any expression. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 5: Polynomials_

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What is meant by the degree of a polynomial in one variable?

  1. Its highest exponent
  2. Its number of terms
  3. Its constant term
  4. Its largest coefficient
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Correct answer: A. Its highest exponent

1. A polynomial in one variable is called univariate. 2. Its degree, also called its order, is the value of the highest exponent it contains. 3. So a cubic has degree three, whatever the coefficients happen to be. 4. The number of terms is a separate idea, and it gives the names monomial, binomial and trinomial. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 5: Polynomials_

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What is the first step when factorising a cubic polynomial by hand?

  1. Divide by the constant term
  2. Guess a root and test it
  3. Complete the square first
  4. Take out the highest power
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Correct answer: B. Guess a root and test it

1. A cubic cannot be factorised by inspection in one move, so one factor has to be found first. 2. Looking at the coefficients suggests small values that might be roots. 3. Each guess is tested by substituting it into the polynomial and checking whether the result is zero. 4. A zero result confirms a root, and the factor theorem then supplies the matching linear factor. 5. Dividing the whole polynomial by its constant term does not produce a factor at all. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 5: Polynomials_

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