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).

Solution:

According to the division algorithm,

Dividend = Divisor × Quotient + Remainder

We have,

Dividend = x³ - 3x² + x + 2, Divisor = g(x), Quotient = x - 2 and Remainder = -2x + 4

Put the given values in the below equation and simplify it, to get the value of g (x).

Dividend = Divisor × Quotient + Remainder

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

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

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

(x³ - 3x² + 3x - 2) = g (x) × (x – 2)

g (x) = (x³ - 3x² + 3x - 2) / (x – 2)

Therefore, g (x) = x² - x + 1

☛ Check: NCERT Solutions Class 10 Maths Chapter 2

Video Solution:

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)

NCERT Solutions Class 10 Maths Chapter 2 Exercise 2.3 Question 4

Summary:

On dividing x³ - 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x - 2 and - 2x + 4, respectively. The value of g (x) is x² - x + 1.

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