Question

4. 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

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Given :-

• Dividend, p(x) = x³ - 3x² + x + 2
• Quotient, q(x) = x - 2
• Remainder, r(x) = - 2x + 4

To find :- Divisor g(x)

Solution:-

By using divison algorithm,

p(x) = g(x) × q(x) + r(x)

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

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

=> g(x) = (x³ - 3x² + 3x - 2) ÷ (x - 2)

=> g(x) = x² - x + 1

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Answer 2

Answer:

this is correct...................