Ineed with these two problems. need an explanation, steps, and an answer.

Let be the scores of the first 8 quizzes. We know that the average of these scores is 85, so we have

The average of the first 9 scores is 81, and it is given by

But we know that the sum of the first 8 is 680:

And we can solve for the nineth score: multiply both sides by 9:

Subtract 680 from both sides:

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!