# Divide 3x^{2} - x^{3} - 3x + 5 by x - 1 - x^{2} , and verify the division algorithm

**Solution:**

We will use the long division method to divide the polynomials

First let us arrange them in the decreasing order of their degree.

Dividend = - x^{3} + 3x^{2} - 3x + 5 and divisor = - x^{2} + x - 1

Division algorithm

Dividend = divisor × quotient + remainder

- x^{3} + 3x^{2} - 3x + 5 = (- x^{2} + x - 1) × (x - 2) + 3

- x^{3} + 3x^{2} - 3x + 5 = - x 3 + x^{2} - x + 2x^{2} - 2x + 2 + 3

- x^{3} + 3x^{2} - 3x + 5 = - x^{3} + 3x^{2} - 3x + 5

LHS = RHS

Thus, verified by the division algorithm

ā Check: NCERT Solutions for Class 10 Maths Chapter 2

## Divide 3x^{2} - x^{3} - 3x + 5 by x - 1 - x^{2} , and verify the division algorithm

**Summary:**

The remainder is 3 when we divide the polynomial 3x^{2} - x^{3} - 3x + 5 by x - 1 - x^{2} , and verified using the division algorithm

**ā Related Questions:**

Math worksheets and

visual curriculum

visual curriculum