SOLUTION: Dear tutor I need your help for my homework. Hope you can help. The question is Find the value of a if 2x-3 is the factor of 2x^4-x^3-3x^2-2x+a

Question 1096119: Dear tutor I need your help for my homework. Hope you can help. The question is
Find the value of a if 2x-3 is the factor of 2x^4-x^3-3x^2-2x+a
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Do polynomial division
=======x^3+x^2-1
2x-3/2x^4-x^3-3x^2-2x+a
=====2x^4-3x^3 (change signs)
==========2x^3-3x^2-2x+a
==========2x^3-3x^2
===================-2x+a
===================-2x+3
change signs to get a-3, which must equal 0, so that a=3
then multiply the factors (2x-3)(x^3+x^2-1), which gives the original polynomial with the last term +3.

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