Question 1038352
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x-2 is to be a factor of 2x³-6x²+5x+a

We divide either by long division or by synthetic division:
and set the remainder = 0

By long division:           By synthetic division

   <u>     2x²-2x+1</u>            2|2 -6  5  a
x-2)2x³-6x²+5x+a             |<u>   4 -4  2</u>
    <u>2x³-4x²</u>                   2 -2  1  a+2
       -2x²+5x
       <u>-2x²+4x</u>
             x+a
             <u>x-2</u>
               a+2

Either way, the remainder is a+2.
We want the remainder to be 0.
So we set a+2 = 0
            a = -2

Edwin</pre></b></font>