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Polynomials Quiz - CBSE Class 7 Mathematics

Free practice quiz: Polynomials (CBSE Class 7 Mathematics). 13 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 7 Mathematics practice quiz has 13 multiple-choice questions on Polynomials, and 13 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

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What Makes a Polynomial

  • A polynomial is a sum of terms, each a number times a variable raised to a whole-number power.
  • Expressions with the variable in a denominator, under a root, or with negative powers are NOT polynomials.
  • By number of terms: one term is a monomial, two terms a binomial, three terms a trinomial.
General form (n is a whole number)
\[p(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0\]
Monomial, binomial, trinomial
\[ax^n,\quad ax^m + bx^n,\quad ax^m + bx^n + c\]

Common mistake: Calling expressions like \frac{1}{x} or \sqrt{x} polynomials. Every power of the variable must be a whole number.

Degree, Coefficients and Constant

  • The degree is the highest power of the variable that appears with a non-zero coefficient.
  • A coefficient is the number multiplied by a power of the variable. The constant term has no variable.
Degree of a_n x^n + ... + a_0 (a_n not zero)
\[\deg p(x) = n\]
Degree of a product
\[\deg\big(p(x)\,q(x)\big) = \deg p(x) + \deg q(x)\]

Common mistake: Taking the first term's power as the degree without checking all terms, or forgetting the sign that belongs with a coefficient.

Value of a Polynomial

  • To find p(a), replace every x with a, then simplify using the correct order of operations.
  • Put brackets around negative values before squaring or cubing them.
Substitution
\[p(x) \to p(a) \text{ by putting } x = a\]
Even power of a negative
\[(-a)^2 = a^2\]
Odd power of a negative
\[(-a)^3 = -a^3\]

Common mistake: Writing -a^2 instead of (-a)^2 when substituting a negative number. Brackets change the sign of the answer.

Zeroes and Factors

  • A number a is a zero of p(x) if p(a) = 0. Then (x - a) is a factor.
  • Split the middle term to factor a quadratic. Set each factor equal to zero to solve the equation.
Factor theorem
\[p(a) = 0 \iff (x - a) \text{ is a factor of } p(x)\]
Splitting the middle term
\[x^2 + (a+b)x + ab = (x+a)(x+b)\]
Difference of squares
\[x^2 - a^2 = (x-a)(x+a)\]
Zero product rule
\[(x-a)(x-b) = 0 \Rightarrow x = a \text{ or } x = b\]

Common mistake: Getting signs wrong. If (x - a) is a factor, the zero is +a, not -a.

Exam tips

Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.

Sample questions

  1. What is a polynomial?

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    Answer: B. An algebraic expression with variables raised to whole number powers

    A polynomial is defined as an algebraic expression that has variables raised only to whole number powers.

  2. What is the degree of the polynomial 4x^3 + 3x + 7?

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    Answer: B. 3

    The degree of a polynomial is the highest power of the variable in it. Here, the highest power is 3 from the term 4x^3.

  3. Which of the following is the factored form of x^2 - 5x + 6?

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    Answer: A. (x - 2)(x - 3)

    To factor x^2 - 5x + 6, we look for two numbers that multiply to 6 and add to -5. These are -2 and -3.

  4. If p(x) = x^3 + 3x^2 - x - 3, what is p(-3)?

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    Answer: B. 0

    Substituting -3 into the polynomial p(-3) = (-3)^3 + 3(-3)^2 - (-3) - 3 = -27 + 27 + 3 - 3 = 0.

  5. Which polynomial is a factor of x^3 - 3x^2 - 4x + 12?

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    Answer: B. x - 3

    Using synthetic division, we can confirm that x - 3 is indeed a factor of the polynomial x^3 - 3x^2 - 4x + 12.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. Which of the following is a polynomial?
  2. Identify the coefficient of x^2 in the polynomial 5x^3 + 4x^2 - 2x + 7.
  3. What do you call a polynomial with one term?
  4. What is the value of the polynomial 2x^2 - 3x + 4 at x = 2?
  5. Determine the zeroes of the polynomial x^2 - 5x + 6.
  6. Which of the following is true for the polynomials f(x) = 2x + 1 and g(x) = x + 2?
  7. Solve the polynomial equation x^2 - 4 = 0.
  8. What is the highest degree of the polynomial 2x^3 - 5x^2 + 7x - 1?

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