Question

When a polynomial f(x)=acx^3+bcx+d, is divided by g(x), it leaves quotient as cx, and remainder as d. The value of g(x)will be _____

(a) -ax^2+b

(b) ax^2-b

(c) ax^2+b

(d) x^2+b

I had been asked this question at a job interview.

This interesting question is from Division of Polynomial in division Polynomials of Mathematics – Class 10

Answer 1

Right choice is (c) ax^2+b

For explanation I would say: We know that,

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.

acx^3 + bcx + d = cx × g(x) + d

acx^3 + bcx + d – d = cx × g(x)

\(\frac {acx^3+bcx}{cx}\)=g(x)

g(x)=ax^2+b