Important Questions: Algebraic Expressions - Free MCQ Test with solutions

An expression that has only one term is called a monomial.
Here, a² is just one term, so it is a monomial.

Why the other options are wrong:

• Option b) Binomial:
  A binomial has two terms joined by addition (+) or subtraction (−).
  Example: x + 3 or a² − b²
  But a² has only one term, so it is not a binomial.

• Option c) Trinomial:
  A trinomial has three terms.
  Example: x² + 2x + 1
  a² has only one term, so it is not a trinomial.

• Option d) Quadrinomial:
  A quadrinomial has four terms.
  Example: p + q + r + s
  a² has only one term, so it is not a quadrinomial.

The coefficient of x² in the expression is (5/7)z.

The coefficient of x in the expression -12x is -12 because the term explicitly includes a negative twelve multiplied by x.

• The expression is 2x² + y² − 3xy + 4.
• Terms are separated by plus or minus signs.
• The individual terms are 2x², y², −3xy, and 4.
• Counting them shows there are 4 terms.
• Thus, the correct answer is c (4).

The value of the expression ax² + by² - cz can be calculated by substituting the given values:
Let a = -2, b = 1, c = -2, x = 1, y = -1, and z = 2.
Calculate each term:

• ax²:
  -2 × (1)² = -2
• by²:
  1 × (-1)² = 1
• cz:
  -2 × 2 = -4
• Combine the results:
  -2 + 1 - (-4) = -2 + 1 + 4 = 3

Thus, the final value of the expression is 3.

The expression a² - b² is a binomial because it consists of two distinct terms:

• a²
• -b²

Each term is separated by an addition or subtraction operator, fitting the definition of a binomial expression.

The expression x³ + y³ + z³ is a trinomial because it consists of three separate terms. Each term includes a different variable, which means they cannot be combined. Therefore, the correct classification is a trinomial.

The value of the expression ax + by + cz can be calculated by substituting the given values:

• Let x = 1, y = -1, z = 2, a = -2, b = 1, and c = -2.
• Substituting these values into the expression:
• ax = -2 * 1 = -2
• by = 1 * (-1) = -1
• cz = -2 * 2 = -4

Now, combine the results:

• -2 + (-1) + (-4) = -2 - 1 - 4 = -7

Thus, the value of the expression is -7.

The coefficient of a variable term includes all constants and variables that multiply the variable. In the expression 5x²yz, the term x² is multiplied by:

• 5
• y
• z

Therefore, the coefficient is 5yz.

The numerical coefficient in an algebraic term is the constant factor that multiplies the variables. In the term 7abc, the numerical coefficient is the number 7, as it is the constant multiplier for the variables a, b, and c.

Therefore, the correct answer is A.