Answer:
A
Explanation:
Fundamental Theorem of Algebra:
This states that any polynomial with degree n will have n solutions which are real or complex.
Since this function you gave has 4 zeroes, this function has to have at at least a degree of 4. The reason I say at least, is because of something called multiplicity. When a zero has an even multiplicity it will have a turning point at the zero, if it has an odd multiplicity it will pass the x-axis. So assuming each zero only has a multiplicity of 1, then this will have at least a degree of 4. It also might have complex zeroes which still count as zeroes.
End Behavior of Polynomial Functions:
So this is pretty easy to remember, but if the leading coefficient is positive, then the end behavior to the right will go up, if it's negative it will go down. Now the next thing to know is an odd degree means that the end behavior will go in opposite directions. So if the right goes up, then the left side will be going down and vice verse. if it's an even degree then the two opposite sides will go in the same direction.
In this case both ends are going down, in the same direction. This means that the leading coefficient is negative and the degree is even.
Using these two things, we can exclude answers
B can't be the answer, it only has 3 zeroes, this has at least 4.
C can't be the answer, it has an odd degree so the end behaviors would go in opposite directions
D can't be the answer, it has a positive leading coefficient so the right side would be going up
This means the only possible equation is A which has at least a degree of 4, negative leading coefficient, and even degree.