Coefficients

Correct answer: B. \(10\)

The numerical coefficient of a monomial is the number multiplied by its variable. In \(10z = 10 \times z\), the number \(10\) is the coefficient of \(z\). Therefore, the correct answer is \(10\). The expression \(10z\) is the complete monomial, while \(z\) is only the variable. Exam tip: identify the numerical factor multiplying the variable.

Correct answer: C. 12

The numerical coefficient of an algebraic term is the number multiplied by the product of its variables. In 12pq, 12 is the numerical part, while pq is the variable part, so the correct answer is 12. In an exam, first separate the numerical part from the variable part.

Correct answer: C. 3

The coefficient of a variable is the numerical factor multiplied by that variable. In the polynomial x² + 3x + 2, the term containing x to the first power is 3x. Since 3x means 3 multiplied by x, the coefficient of x is 3, making option C correct. The number 1 is the understood coefficient of x², not of x. The number 2 is the constant term because it contains no variable. The expression x² is another term with a different power of x, so it cannot be the numerical coefficient of the first-power x term. Identifying the exact requested term avoids confusing coefficients with terms or constants.