SOLUTION: The expressions x³+ax²-x+b and x³+bx²-5x+3a have a common factor x+2. Find the value of a and b.

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Question 696488: The expressions x³+ax²-x+b and x³+bx²-5x+3a have a common factor x+2. Find the value of a and b.
Answer by Edwin McCravy(20066)   (Show Source): You can put this solution on YOUR website!
The expressions x³+ax²-x+b and x³+bx²-5x+3a have a common factor x+2. Find the value of a and b.
Since each has a common factor of x+2, -2 is a zero 
of each polynomial.  Therefore if we substitute x=-2
in each we will get 0.

                   x³+ax²-x+b      x³+bx²-5x+3a
          (-2)³+a(-2)²-(-2)+b=0    (-2)³+b(-2)²-5(-2)+3a=0
                  -8+a(4)+2+b=0            -8+b(4)+10+3a=0
                      -6+4a+b=0                  2+4b+3a=0
                         4a+b=6                    3a+4b=-2                     
    
Solve the system of equation:

4a+ b= 6
3a+4b=-2

Get a=2, b=-2.

Edwin
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