on dividing x cube minus 3 X square + X + 2 by a polynomial g(X )the quotient and remainder were x -2 and - 2 X + 4 respectively find G(X)
Answers
Given : Dividing x³ - 3x² + x + 2 by g(x) the quotient and remainder were x - 2 and -2x + 4
To Find : g(x)
Solution:
x³ - 3x² + x + 2 = g(x) (x - 2) + (-2x + 4)
=> g(x) (x - 2) = x³ - 3x² + 3x -2
=> g(x) = (x³ - 3x² + 3x -2)/(x 2)
x² -x + 1
x - 2 _| (x³ - 3x² + 3x -2) |_
x³ - 2x²
__________
-x² + 3x - 2
-x² + 2x
____________
x - 2
x - 2
____________
0
g(x) = x² -x + 1
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This is the answer hope it helps
