# On dividing x^{3} - 3x^{2} + 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 = x^{3} - 3x^{2} + 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

(x^{3} - 3x^{2} + x + 2) = g (x) × (x - 2) + (- 2x + 4)

(x^{3} - 3x^{2} + x + 2) - (- 2x + 4) = g (x) × (x - 2)

(x^{3} - 3x^{2} + x + 2x + 2 - 4) = g (x) × (x - 2)

(x^{3} - 3x^{2} + 3x - 2) = g (x) × (x – 2)

g (x) = (x^{3} - 3x^{2} + 3x - 2) / (x – 2)

Therefore, g (x) = x^{2} - 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 x^{2} - x + 1.

**☛ Related Questions:**

- Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:(i) p(x) = x3 - 3x2 + 5x - 3, g(x) = x2 - 2(ii) p(x) = x4 - 3x2 + 4x + 5, g(x) = x2 + 1 - x(iii) p(x) = x4 - 5x + 6, g(x) = 2 - x2
- Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:(i) t2 - 3, 2t4 + 3t3 - 2t2 - 9t - 12(ii) x2 + 3x + 1, 3x4 + 5x3 - 7x2 + 2x + 2(iii) x3 - 3x + 1, x5 - 4x3 + x2 + 3x + 1
- Obtain all other zeroes of 3x4 + 6x3 - 2x2 - 10x - 5, if two of its zeroes are √ 5/3 and - √ 5/3
- Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i) deg-p(x) = deg q(x) (ii) deg q(x) = deg r (x) (iii) deg r (x) = 0

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