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On dividing x^3-3x^2+x+2by a polynomial ...

On dividing `x^3-3x^2+x+2`by a polynomial the quotient and remainder were `x-2`and `-2x+4`, respectively. Find g(x).

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To find the polynomial \( g(x) \) given that dividing \( x^3 - 3x^2 + x + 2 \) by \( g(x) \) yields a quotient of \( x - 2 \) and a remainder of \( -2x + 4 \), we can use the polynomial division algorithm. ### Step-by-Step Solution 1. **Write the Division Algorithm**: According to the polynomial division algorithm, we have: \[ \text{Dividend} = \text{Divisor} \times \text{Quotient} + \text{Remainder} \] ...
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