On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 nd –2x + 4, respectively. Find g(x).
Given ,
Dividend p(x) = x3 - 3x2 + x + 2
Quotient = x – 2
Remainder = -2x + 4
Let divisor = g(x)
As we know ,
Dividend = Divisor × Quotient + Remainder
x3- 3x2 +x+ 2 = g(x) × (x – 2) + (-2x + 4)
x 3- 3x2 + x + 2 – (-2x + 4) = g(x) × (x – 2 )
Therefore, g(x) × (x – 2 ) = x3 – x2 + x + 2
Now we will divide p(x) by quotient x – 2 to find divisor g(x)
Therefore , g(x) = ( x2 – x + 1 )
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