Question

If f(x) is divided by g(x), g(x) ≠ 0 , then there exist two polynomials q(x) and r(x) such that

• A. q(x) = f(x) g(x) - r(x)
• B. f(x) = g (x) q (x) + r (x)
• C. g(x) = f(x) q (x) + r (x)
• D. r(x) = f(x) g(x) + q(x)

Answer 1

The correct option is B

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

According to division algorithm

Dividend = Divisor x Quotient + Remainder

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