On dividing x3 – 3x2 + 4x + 5 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).
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dividend=divisor x quotient + remainder
x3-3x2+4x+5=g(x) x( x-2) +(-2x+4)
x3-3x2+4x+5 \ x-2 =g(x)+(-2x+4)
x3-x+2=g(x)+(-2x+4)
x3-x+2+2x-4=g(x)
x3+x-6=g(x)
x3-3x2+4x+5=g(x) x( x-2) +(-2x+4)
x3-3x2+4x+5 \ x-2 =g(x)+(-2x+4)
x3-x+2=g(x)+(-2x+4)
x3-x+2+2x-4=g(x)
x3+x-6=g(x)
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