For what value of #b# will the polynomial #P(x) = 4x^3-3x^2+bx+6# have the same remainder when it is divided by both #x# and #x+3#?

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Answer 1 · 2018-01-26T14:45:41

#b=-45#

The remainder when divided by #x-a# is #P(a)#

So we require #P(0) = P(-3)#

#P(0) = 6#

#P(-3) = 4(-27)-3(9)+b(-3)+6 = -108-27-3b+6 = -3b-129#

So we need:

#6 = P(0) = P(-3) = -3b-129#

Adding #3b-6# to both ends this becomes:

#3b = -135#

Then dividing both sides by #3# we find:

#b = -45#