Answer:
Option a. x - y^2 - 3y
Step-by-step explanation:
<u><em>The options of the questions are</em></u>
a. x - y^2 - 3y
b. x - 3y + 6
c. x + 3y^2 + 3y
d. x + 3y + 7
we know that
The expression has 3 terms
The y-term has a coefficient of negative 3 and the x-term has a coefficient of one
The expression does not have a constant term
<u><em>Verify each case</em></u>
case a) we have x - y^2 - 3y
The expression has 3 terms ----> is ok
The y-term has a coefficient of negative 3 ---> is ok
The x-term has a coefficient of one ----> is ok
The expression does not have a constant term ----> is ok
therefore
She could have written this expression
case b) we have x - 3y + 6
The expression has 3 terms ----> is ok
The y-term has a coefficient of negative 3 ---> is ok
The x-term has a coefficient of one ----> is ok
The expression does not have a constant term ---> is not ok (the expression have a constant term of 6)
therefore
She couldn't have written this expression
case c) we have x + 3y^2 + 3y
The expression has 3 terms ----> is ok
The y-term has a coefficient of negative 3 ---> is not ok (the y-term has a coefficient of positive 3)
therefore
She couldn't have written this expression
case d) we have x + 3y + 7
The expression has 3 terms ----> is ok
The y-term has a coefficient of negative 3 ---> is not ok (the y-term has a coefficient of positive 3)
therefore
She couldn't have written this expression
