How do you determine the value of k if the remainder is 3 given #(x^3+x^2+kx-15) div(x-2)#?

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Answer 1 · 2016-12-24T01:33:20

Use the remainder theorem to find #k = 3#

Let #f(x) = x^3+x^2+kx-15#

By the remainder theorem, the remainder when #f(x)# is divided by #(x-2)# will be #f(2)#

So we have:

#3 = f(2) = 8+4+2k-15 = 2k-3#

Add #3# to both ends to get:

#6 = 2k#

Divide both sides by #2# and transpose to get:

#k = 3#