without actual division prove that 2x⁴-6x³+3x²+3x-2 is exactly divisible by x²-3x+2
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Step-by-step explanation:
2x⁴-6x³+3x²+3x-2=
(2x⁴-6x³+4x²)-(x²-3x+2)=
2x(x²-3x+2) - (x²-3x+2)=
(2x-1)(x²-3x+2)
As we see (x²-3x+2) is a factor so divisibility is confirmed
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