Question

What is the remainder when the polynomial (see picture) is divided by x+5?

Answer 1

Answer: 60

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To get this answer, we plug x = -5 into the polynomial function below. This is using the remainder theorem which says "dividing p(x) by x-k will lead to a remainder of r = p(k)". In this case, x+5 = x-(-5) = x-k so k = 5.

Replace every x with -5 to get...

p(x) = 5x^2 + 10x - 15

p(-5) = 5(-5)^2 + 10(-5) - 15

p(-5) =5(25) + 10(-5) - 15

p(-5) = 125 - 50 - 15

p(-5) = 75 - 15

p(-5) = 60

Another way to get this answer is to use either polynomial long division (see figure 1) or synthetic division (see figure 2). Both figures are attached as images below.