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

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.

the answer is 1/4

step-by-step explanation: