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

Answer:

Given ,

Dividend p(x) = x³- 3x² + x + 2

Quotient = x – 2

Remainder = -2x + 4

Let divisor = g(x)

As we know ,

Dividend = Divisor × Quotient + Remainder

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

x ³- 3x²+ x + 2 – (-2x + 4) = g(x) × (x – 2 )

Therefore, g(x) × (x – 2 ) = x³ – x²+ x + 2

Now we will divide p(x) by quotient x – 2 to find divisor g(x)

Therefore , g(x) = ( x² – x + 1 )

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

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

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