Question

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

Answer 1

Answer:

x²  - x + 1

Step-by-step explanation:

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

f(x) = g(x)q(x) + r(x)

f(x) = x³-3x²+x+2

q(x) = x - 2

r(x) = -2x + 4

let say g(x) = (ax² + bx + c)

g(x)q(x) + r(x)

=  (ax² + bx + c)(x - 2)  + (-2x - 4)

= ax³ - (2a - b)x² + (c -2b)x -2c  -2x +4

= ax³ - (2a - b)x² + (c -2b-2)x  - 2c  + 4

Comparing with

x³-3x²+x+2

a = 1

2a - b = 3  => b = -1

c - 2b - 2 = 1

=> c +2 - 2 = 1

=> c = 1

g(x) = (x²  - x + 1)

Answer 2

Quotient :- x²+x-5

Remainder :- x-2.

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