Without actual division, prove that 2x 4 -5x 3 +2x 2 -x+2 is divisible by x 2 -3x+2.
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x2-3x+2 = (x-2)(x-1)
P(x)=2x 4 -5x 3 +2x 2 -x+2 is divisible by x 2 -3x+2 is equivalent to
1 and 2 are zeros for 2x 4 -5x 3 +2x 2 -x+2
we can verify thatP(1) = 0
and P(2)=0
then
2x 4 -5x 3 +2x 2 -x+2 is divisible by x 2 -3x+2
P(x)=2x 4 -5x 3 +2x 2 -x+2 is divisible by x 2 -3x+2 is equivalent to
1 and 2 are zeros for 2x 4 -5x 3 +2x 2 -x+2
we can verify thatP(1) = 0
and P(2)=0
then
2x 4 -5x 3 +2x 2 -x+2 is divisible by x 2 -3x+2
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