Question

The polynomial P is graphed.

Answer 1

Answer:  Remainder = 3

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Explanation:

The remainder theorem says that if we divide some polynomial p(x) over (x-k), then p(k) is the remainder.

The expression x+1 is the same as x-(-1). Comparing this to x-k shows k = -1.

So we'll need to evaluate p(-1)

To do so visually, draw a vertical line through -1 on the x axis. Make sure this vertical line crosses the blue curve at some point, which I'll call point A.

From point A, draw a horizontal line to the y axis. You should reach y = 3.

This is all shown in the diagram below.

In other words, the point (-1,3) is on the blue curve, and p(-1) = 3.

So the remainder is 3.