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Oneta writes an algebraic expression with three terms. The \( y \)-term has a coefficient of -3, and the \( x \)-term has a coefficient of 1. The expression does not have a constant term. Which expression could she have written?

A. \( x - y^2 - 3y \)

B. \( x - 3y + 6 \)

C. \( x + 3y^2 + 3y \)

D. [tex]\( x + 3y + 7 \)[/tex]

Sagot :

GinnyAnswer
To determine which algebraic expression Oneta could have written given the constraints:

1. The [tex]$y$[/tex]-term has a coefficient of -3.
2. The [tex]$x$[/tex]-term has a coefficient of 1.
3. The expression does not have a constant term.

Let's analyze the given options one by one:

1. \( x - y^2 - 3y \):
- The [tex]$x$[/tex]-term has a coefficient of 1, which matches the given condition.
- The [tex]$y$[/tex]-term here is \(-3y\), which has a coefficient of -3, also matching the given condition.
- There is no constant term in the expression.
- Therefore, this expression fits all the given criteria.

2. \( x - 3y + 6 \):
- The [tex]$x$[/tex]-term has a coefficient of 1, which matches the condition.
- The [tex]$y$[/tex]-term has a coefficient of -3, which also matches the condition.
- However, the expression includes a constant term of 6, which does not fit the condition of having no constant term.
- Therefore, this expression does not meet all the criteria.

3. \( x + 3y^2 + 3y \):
- The [tex]$x$[/tex]-term has a coefficient of 1, which matches the condition.
- The [tex]$y$[/tex]-term has a coefficient of 3, not -3.
- There is no constant term in the expression.
- Therefore, this expression does not meet the criteria regarding the [tex]$y$[/tex]-term's coefficient.

4. \( x + 3y + 7 \):
- The [tex]$x$[/tex]-term has a coefficient of 1, which matches the condition.
- The [tex]$y$[/tex]-term has a coefficient of 3, not -3.
- The expression includes a constant term of 7, which does not fit the condition of having no constant term.
- Therefore, this expression does not meet multiple criteria.

From the analysis above, the only expression that matches all the conditions given is:

[tex]\[ x - y^2 - 3y \][/tex]

So, Oneta could have written the expression [tex]\( x - y^2 - 3y \)[/tex].
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