Question

The real number that should be subtracted from the polynomial f(x)=15x^5+70x^4+35x^3-135x^2-40x-11 so that it is exactly divisible by 5x^4+10x^3-15x^2-5x is ____________

(a) -12

(b) -11

(c) 11

(d) 12

This question was posed to me in homework.

This intriguing question comes from Division of Polynomial in section Polynomials of Mathematics – Class 10

Answer 1

Correct choice is (b) -11

The explanation is: On dividing, 15x^5+70x^4+35x^3-135x^2-40x-11 by 5x^4+10x^3-15x^2-5x

We get, 3x+8 as quotient and remainder as -11.

So if we subtract -11 from 15x^5+70x^4+35x^3-135x^2-40x-11 it will be exactly divisible by 5x^4+10x^3-15x^2-5x.