Let's analyze each expression option to determine which one Oneta could have written, based on the given conditions:
1. Expression: [tex]\( x - y^2 - 3y \)[/tex]
- Number of terms: 3
- [tex]\( x \)[/tex] term with coefficient 1
- [tex]\( -y^2 \)[/tex] term (this term is independent of our conditions as it's a [tex]\( y^2 \)[/tex] term)
- [tex]\( -3y \)[/tex] term with coefficient -3
- No constant term: Correct
2. Expression: [tex]\( x - 3y + 6 \)[/tex]
- Number of terms: 3
- [tex]\( x \)[/tex] term with coefficient 1
- [tex]\( -3y \)[/tex] term with coefficient -3
- [tex]\( 6 \)[/tex] term which is a constant term
- No constant term: Incorrect (contains a constant term)
3. Expression: [tex]\( x + 3y^2 + 3y \)[/tex]
- Number of terms: 3
- [tex]\( x \)[/tex] term with coefficient 1
- [tex]\( 3y^2 \)[/tex] term (again, this term is independent of our conditions as it's a [tex]\( y^2 \)[/tex] term)
- [tex]\( 3y \)[/tex] term with coefficient 3
- No constant term: Correct
- y-term has coefficient -3: Incorrect (coefficient of [tex]\( y \)[/tex] term is 3)
4. Expression: [tex]\( x + 3y + 7 \)[/tex]
- Number of terms: 3
- [tex]\( x \)[/tex] term with coefficient 1
- [tex]\( 3y \)[/tex] term with coefficient 3
- [tex]\( 7 \)[/tex] term which is a constant term
- No constant term: Incorrect (contains a constant term)
- y-term has coefficient -3: Incorrect (coefficient of [tex]\( y \)[/tex] term is 3)
From the above analysis, only the first expression meets all the given conditions:
- The [tex]\( y \)[/tex]-term has a coefficient of -3
- The [tex]\( x \)[/tex]-term has a coefficient of 1
- There is no constant term.
Thus, the expression Oneta could have written is:
[tex]\[ x - y^2 - 3y \][/tex]
