If synthetic division reveals a zero, why should we try that value again as a possible solution? - polynomial functions can have imaginary zeros, so if it is an imaginary zero, it could also be a real zero. - polynomial functions can have repeated zeros, so the fact that a number is a zero doesn't preclude it being a zero again. - polynomial functions can have real zeros, so the fact that a number is a real zero means it could also be an imaginary zero. - polynomial functions can have imaginary zeros, so if it is a zero, it could also be an imaginary zero. - polynomial functions can have rational zeros, so trying a value again can find irrational zeros.

The correct option is:

Polynomial functions can have repeated zeros, so the fact that a number is a zero doesn't preclude it being a zero again.

Step-by-step explanation:

As we know that if we get a zero of a polynomial than that particular zero could also be a zero of multiplicity greater than one or in short we can say that it is a repeated zero of the polynomial.

Hence, in order to check that it is a repeated zero we factorize the polynomial and see that it is a zero of the other factor or not if it is a zero of the other factor then we will say that the zero is a repeated zero of the polynomial.

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)