Question

If f(x) is divided by g(x), it gives quotient as q(x) and remainder as r(x). Then,  f(x)=q(x)×g(x)+r(x) where, f(x) is the dividend, q(x) is the quotient, g(x) is the divisor and r(x) is the remainder.

(a) True

(b) False

I had been asked this question in my homework.

Question is from Division of Polynomial in section Polynomials of Mathematics – Class 10

Answer 1

Right answer is (a) True

To explain I would say: Consider, f(x) is 27x^2-39x, q(x) as 9x+2, g(x) as 3x-5 and remainder is 10.

f(x)=q(x)×g(x)+r(x)

RHS

q(x)×g(x)+r(x)=(9x+2)(3x-5)+10=27x^2-45x+6x-10+10=27x^2-39x, which is equal to LHS.

Hence proved.