Question

बहु पदों के लिए विभाजन एल्गोरिथ्म का कथन लिखिए तथा एक उदाहरण देकर इसकी सत्यता की जांच कीजिए​

Answer 1

SOLUTION

TO DETERMINE

The statement of division algorithm for multiple terms and check its correctness by giving an example.

EVALUATION

Division Algorithm

Let f(x) and g(x) be two polynomials of degree n and m respectively and n ≥ m . Then there exist two uniquely determined polynomials q(x) and r(x) satisfying

f(x) = g(x) q(x) + r(x)

Where the degree of q(x) is n - m and r(x) is either a zero polynomial or the degree of r(x) is less than m

VERIFICATION :

Let f(x) = x³ - 3x² + 3x - 1

g(x) = x² - 2x + 1

Then q(x) = x - 1 , r(x) = 0

Such that f(x) = g(x) q(x) + r(x)

Degree of f(x) = 3

Degree of g(x) = 2

Also degree of q(x) = 1 = 3 - 2

r(x) is a zero polynomial

Hence verified

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