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Divide 3x2 - x3 - 3x + 5 by x - 1 - x2 , 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 = - x3 + 3x2 - 3x + 5 and divisor = - x2 + x - 1
Division algorithm
Dividend = divisor × quotient + remainder
- x3 + 3x2 - 3x + 5 = (- x2 + x - 1) × (x - 2) + 3
- x3 + 3x2 - 3x + 5 = - x 3 + x2 - x + 2x2 - 2x + 2 + 3
- x3 + 3x2 - 3x + 5 = - x3 + 3x2 - 3x + 5
LHS = RHS
Thus, verified by the division algorithm
☛ Check: NCERT Solutions for Class 10 Maths Chapter 2
Divide 3x2 - x3 - 3x + 5 by x - 1 - x2 , and verify the division algorithm
Summary:
The remainder is 3 when we divide the polynomial 3x2 - x3 - 3x + 5 by x - 1 - x2 , and verified using the division algorithm
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