Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x) .q(x)+ r(x), where degree r (x) = 0.

AlanjexB AlanjexB Best Answer 1 year ago

ESTION ✪✪||Give an example of polynomials f(X), g(x), q(x) and r(x) SATISFYING f(x) = g(x) .q(x)+ r(x), where DEGREE r (x) = 0 ? || ✰✰ ANSWER ✰✰ ||Let f(x) = 2x⁴ + 8x³ + 6x² +4x +12→ q(x) = 2→ g(x) = x⁴ + 4x³ + 3x² + 2x + 1→ r(x) = 10Here, degree r(x) = 0Now, we know that :-- According to EUCLID division lemma :-a = bq + r where 0 ≤ r < B Hence, Let P(x), g(x) , q(x), and r(x) satisfy EUCLID division lemma .Then, P(x) = g(x) × Q(x) + r(x) where, 0≤ r(x) < g(x)Dividend = Divisor × Quotient + RemainderPutting values now, f(x) = q(x) × g(x) + r(x)→ 2( x⁴ + 4x³ + 3x² + 2x + 1) + 10→ 2x⁴ + 8x³ + 6x² +4x + 2 +10→ 2x⁴ + 8x³ + 6x² +4x +12Hence, above values of f(x) ,q(x) , g(x) and r(x) satisfy the division algorithm.

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