Question

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

Answer 1

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Answer 2

lets the g(X) = Y

Y = [ ( X³ - 3X² + X + 2 ) - ( -2x + 4 ) ] ÷ X - 2

Y = [ ( X³ - 3X² + X + 2 ) + 2x - 4 ] ÷ X - 2

Y = X³ - 3X² + 3X - 2 ÷ X - 2

Y = X² - X + 1

proof = ( X² - X + 1 × X - 2 ) + ( - 2x + 4 )

= X³ - X² - X - 2X² + 2X - 2 - 2X + 4

= X³ - 3X² + X + 2