Question

In -6xy, the coefficient of x is 6y.
A. True
B. False
C. Ambiguous
D. Data insufficient

Answer 1

Hint: In this question, we are given a term -6xy and we need to check if the coefficient of x for this term is 6y or not. For this, we will first understand what is a coefficient. After that, we will remove x from the given term. The remaining term will be our coefficient. From that, we can check and evaluate our answers.

Complete step by step answer:
Here we are given the term as -6xy.
Let us first understand the meaning of a coefficient. In mathematics, a coefficient is a multiplicative factor in some terms of a polynomial, a series, or any expression. A coefficient is usually a number but it can be variable too.
For finding coefficients of a given term, the easiest way is to remove the variable of which coefficient is to be found and the remaining part will be our required coefficient. Here the term is -6xy.
Since it involves variables and negative signs. When we remove x from the term (of which coefficient is to be found) we get the remaining term as -6y. Hence the coefficient of -6xy is -6y. But we are given the coefficient of -6xy as 6y which is not true.
Hence the given statement is false.
Hence option B is the correct answer.

Note:
Students should note that a negative sign is also considered as a multiplicative factor, so it is a part of the coefficient. Students often make mistakes of ignoring variables as the coefficient of other variables. Here -6y is the coefficient of -6xy. If we had to find the coefficient of y in -6xy, our answer would be -6x.