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Terms, Factors, and Coefficients Quiz - CBSE Class 8 Mathematics

Free practice quiz: Terms, Factors, and Coefficients (CBSE Class 8 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 8 Mathematics practice quiz has 17 multiple-choice questions on Terms, Factors, and Coefficients, and 17 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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Terms and the Constant Term

  • An expression is made of terms joined by + or - signs.
  • Each term keeps the sign written just before it.
  • A term with no variable is called the constant term.
Terms of an expression
\[ap + bq - c \;\Rightarrow\; \text{terms: } ap,\ bq,\ -c\]
Constant term
\[\text{In } px^{2} + qx + r,\ \text{the constant term is } r\]

Common mistake: Forgetting the minus sign, for example writing the term as c instead of -c, or not counting the constant as a term.

Factors of a Term

  • A term is a product of factors: a number and variables.
  • Write each power as repeated multiplication to list every variable factor separately.
Power as repeated factors
\[a^{m} = \underbrace{a \times a \times \cdots \times a}_{m \text{ times}}\]
Factors of a term
\[9p^{2}q = 9 \times p \times p \times q\]

Common mistake: Writing p² as a single factor instead of p × p, or leaving out the numerical factor.

Coefficient of a Term

  • The coefficient is the numerical factor of a term, including its sign.
  • If no number is written, the coefficient is 1, or -1 if there is a minus sign.
Numerical coefficient
\[\text{In } -11m^{2}n,\ \text{the coefficient of } m^{2}n \text{ is } -11\]
Hidden coefficient
\[x = 1 \cdot x, \quad -y = (-1) \cdot y\]
Missing term
\[\text{If no } x^{k} \text{ term appears, its coefficient is } 0\]

Common mistake: Dropping the negative sign, or confusing terms like a²b and ab², which have different powers on each variable.

Like Terms and Expanding Brackets

  • Like terms have the same variables raised to the same powers.
  • Expand brackets first, then add the coefficients of like terms.
  • Count terms or read coefficients only after combining like terms.
Combining like terms
\[mx^{2}y + nx^{2}y = (m+n)x^{2}y\]
Distributive law
\[a(b + c) = ab + ac\]
Product of two binomials
\[(p + q)(r + s) = pr + ps + qr + qs\]

Common mistake: Counting terms before combining like terms, or treating xy² and x²y as like terms.

Exam tips

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

Sample questions

  1. Identify the coefficient of 'x' in the expression 5x + 3y.

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    Answer: B. 5

    The coefficient of a variable is the number multiplied by it. In 5x + 3y, 5 is multiplied by x, so 5 is the coefficient of x.

  2. What is the constant term in the expression 2x² + 5x - 8?

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    Answer: C. -8

    A constant term is a term without any variables. In this expression, -8 is the constant term.

  3. Find the factors of the expression 15x³y²z.

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    Answer: C. 15, x³, y², z

    The factors are the numbers and variables that multiply together to form the expression. It can also be written as 3 x 5 x x x x x y x y x z.

  4. Determine the number of factors in the expression 24a⁴b²c³.

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    Answer: D. 10

    The factors are 2, 2, 2, 3, a, a, a, a, b, b, c, c, c. Therefore, there are 10 factors.

  5. In the expression (a + b)² = a² + 2ab + b², identify the coefficient of 'ab'.

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    Answer: B. 2

    The coefficient of 'ab' in the expansion of (a + b)² is 2.

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More questions in this quiz

Answers and explanations are in the full quiz.

  1. What are the factors of the term 6xy?
  2. In the expression 7ab - 4c + 2, how many terms are there?
  3. Identify the factors of 12a²b³.
  4. What is the coefficient of x²y in the expression 3x²y + 7xy² - 2?
  5. If the expression is 4x³ - 6x² + 2x + 5, what is the coefficient of x²?
  6. What are the terms in the expression -3a²bc + 5ab²c - 7abc² + 12?
  7. Given the expression 2x³y²z - 5x²yz³ + 3xyz, find the coefficient of x²yz³.
  8. Simplify the expression: 5(2x²y - 3xy²) + 2(x²y + 4xy²) and identify the coefficient of xy².
  9. Find the constant term in the expression (3x - 2)(2x + 5) after expansion.
  10. If (x + y)(x - y) = x² - y², what is the coefficient of the 'xy' term?
  11. Given that (a + b)³ = a³ + 3a²b + 3ab² + b³, find the coefficient of a²b.
  12. Determine the number of terms in the expansion of (a + b + c)⁴

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