For what value of c will the polynomial #P(x)=-2x^3+cx^2-5x+2# have the same remainder when it is divided by x-2 and x+1?

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Answer 1 · 2017-01-08T20:25:38

#c = 11#

The remainder theorem states that when a polynomial #p(x)# is divided by #x - a#, the remainder is given by #p(a)#.

Thus, the remainder when #P(x)# is divide by #x - 2# is #-2(2)^3 + c(2)^2 - 5(2) + 2 = -16 + 4c - 10 + 2 = -24 + 4c#

The remainder when #P(x)# is divided by #x + 1# is #-2(-1)^3 + c(-1)^2 - 5(-1) + 2 = 2 + c + 5 + 2 = 9 + c#

Setting the two as being equal, we have:

#-24 + 4c = 9 + c#

#3c = 33#

#c = 11#

Hopefully this helps!