Answer:
A.-[tex]2x^2[/tex]
D.[tex]5x^2[/tex]
E.[tex]x^2[/tex]
Step-by-step explanation:
Like terms must have the same variable, in this case x, and the same exponent, in this case 2. Since the original term is [tex]3x^2[/tex], the like terms will be those that contain [tex]x^2[/tex], regardless of whether their coefficient or sign is different.
Analyzing the options:
A.-[tex]2x^2[/tex]
We have the same variable and the same exponent [tex]x^2[/tex], so it is a like term.
B. [tex]3x[/tex]
You have the same variable x but not the same exponent. So it's not a like term of [tex]3x^2[/tex]
C.[tex]3x^3[/tex]
Same variable [tex]x[/tex] but as in the previous case, the exponent is different, it is a 3 and it should be a 2, so it is not a similar or like term.
D.[tex]5x^2[/tex]
In this option we do have the [tex]x^2[/tex], so it is a like term of [tex]3x^2[/tex]
E.[tex]x^2[/tex]
It is also a like term because it contains the [tex]x^2[/tex].
In summary the like terms are:
A.-[tex]2x^2[/tex]
D.[tex]5x^2[/tex]
E.[tex]x^2[/tex]
