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In this text book, it was mentioned that we generally use the term coefficient in two ways

1) The numerical coefficient of a term in an algebraic expression

2) A variable as a coefficient for rest of the term

But didn't comment anything on splitting exponent on a variable.

Example: Let $5x^2+9xy$ be the algebraic expression under consideration

then it is clear for me that 5 is coefficient for the term $5x^2$ as well as $x^2$

$9$ is the coefficient for the term $9xy$ as well as $xy$

$x$ is the coefficient for $9y$ and $y$ is the coefficient for $9x$ in the term $9xy$.

But confused on whether I can call $x$ as the coefficient of $5x$ in the term $5x^2$ or not because the textbook didn't provide any example like this.

hanugm
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1 Answers1

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It would depend on what term you're considering the main variable. If you only have one variable, you can't call the main variable a coefficient - but it is a factor of the original. That is, $5x$ is not the coefficient of $5x^2$, but it is a factor (the other being just plain $x$).

If you have more than one variable and you're considering the second variable as a constant, then you'd be able the numerical and constant variable as the coefficient.

For example, if we have $5xy^2$ and $y$ is the main variable and $x$ is a constant, then indeed $5x$ can be considered the coefficient. If $x$ is the main variable and $y$ is a constant, $5y^2$ can be considered the coefficient.

bjcolby15
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