by the remainder theorem, what can be said about the polynomial function z(x) if the remainder is 1 when z(x) is divided by x-4. z( )=_________

Answer 1

The "zero" associated with "x - 4" is "4"

So, the remainder theorem says that z(4) = 1

Answer 2

Answer: z(4) = 1.

Even though we don't have an explicit rule for z(x), we can still answer the question.

Since 4 is what makes x - 4 = 0, 4 is what we plug in to z(x) to get the remainder of 1.

I am making the following function up to demonstrate.

Let f(x) = x² - 2x -17, and suppose we want to divide it by x + 5.

Then using x = -5 (since this would make x + 5 = 0),

we have

f(-5) = (-5)² - 2(-5) - 17

= 25 +10 - 17

= 18...which would be the remainder if you were to do the division.

Synthetically dividing, it would look like

-5 | 1 -2 -17

-5 35

--------------------------

1 -7 18

And so we get 18 for the remainder.

That is, f(-5) = 18.