When the expression #2x^3 + ax^2 -5x -2# is divided by #2x-1#, the remainder is #-3.5# . Determine the value of the constant #a#. Can someone please help?

Question

When the expression #2x^3 + ax^2 -5x -2# is divided by #2x-1#, the remainder is #-3.5# . Determine the value of the constant #a#.

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Answer 1 · 2018-05-21T22:09:36

#a = 3#

The remainder theorem states that if #P(x)# is divided by #x - a#, then the remainder is given by #P(a)#.

Therefore:

#2(1/2)^3 + a(1/2)^2 - 5(1/2) - 2 = -3.5#

A little bit of algebra lets us simplify to

#2(1/8) + a(1/4) - 5/2 = -1.5#

#1/4a = -3/2 + 5/2 - 1/4#

#4(1/4a) = 4(-3/2 + 5/2 - 1/4)#

#a = -6 + 10 - 1#

#a = 3#

Hopefully this helps1