IMO Olympiad Work Book 9>Polynomials>Remainder Theorem

Remainder Theorem

Author:Mahabir Singh

9th Foundation

IMPORTANT

Important Questions on Remainder Theorem

MEDIUM

IMPORTANT

IMO Olympiad Work Book 9>Polynomials>Remainder Theorem> Q 1

If ${(5 x^{2} + 14 x + 2)}^{2} - ({4 x^{2} - 5 x + 7)}^{2}$ is divided by $(x^{2} + x + 1),$ then the quotient $' q'$ and remainder $' r'$ are _______

MEDIUM

IMPORTANT

IMO Olympiad Work Book 9>Polynomials>Remainder Theorem> Q 2

Find the remainder when the expression $3 x^{3} + 8 x^{2} - 6 x + 1$ is divided by $x + 3$

MEDIUM

IMPORTANT

IMO Olympiad Work Book 9>Polynomials>Remainder Theorem> Q 3

Value of R , if
$\frac{a^{2} - 19 a - 25}{a - 7} = a - 12 + \frac{R}{a - 7}$

MEDIUM

IMPORTANT

IMO Olympiad Work Book 9>Polynomials>Remainder Theorem> Q 4

Given that $x = 2$ is a solution of $x^{3} - 7 x + 6 = 0$ . The other solution s are ____

MEDIUM

IMPORTANT

IMO Olympiad Work Book 9>Polynomials>Remainder Theorem> Q 5

When $p (x) = x^{3} + a x^{2} + 2 x + a$ is divided by $(x + a)$ , the remainder is __________

MEDIUM

IMPORTANT

IMO Olympiad Work Book 9>Polynomials>Remainder Theorem> Q 6

The remainder when $x^{4} - y^{4}$ is divided by $x - y$ is __________