Question

On dividing x3
-3x2
+x+2 by a polynomial g(x), the quotient and remainder were
x-2 and -2x+4 respectively. Find g(x)

Answer 1

Answer:

g(x) = x² - x + 1

Step-by-step explanation:

x³ - 3x² + x + 2 = ( x - 2 ) g(x) - 2x + 4

=> ( x - 2 ) ( x² - x - 1) = ( x - 2 ) g(x) - 2( x - 2 )

=> x² - x - 1 = g(x) - 2

=> g(x) = x² - x + 1