Use synthetic division to find the value of p and q if x+1 and x-2 are the factors of x3+ px2 + qx + 6
2 answers:
Set up synth. div. in the usual way. If x-2 is a factor of the given polynomial, use +2 as the divisor in synth. div.: ______________________________ 2 / 1 p q 6 _______+2______2p+4____________________ 1 p+2 2p+q+4 Finish this. Note that if 2 is a root and x-2 is a factor, the final result MUST equal 0. Thus, we get the equation p-q=5. Do the same thing for the root -1 (which comes from the factor (x+1). You'll end up with two linear equations which can be solved for p and q. Substitute these values of p and q into the given polynomial. p=-4, so that polynomial becomes x^3 - 4x + q + 6. I did this, and found that -1 and +2 are indeed roots of the resulting polynomial.
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