Remainder Theorem
Remainder Theorem: Overview
This topic explains the concept of dividend, quotient, divisor and remainder with various examples. We will also learn the basic formula related to this concept. It also discusses the proof of the remainder theorem.
Important Questions on Remainder Theorem
and , find the remainder when is divided by .
Find the remainder when dividend and divisor are given.
Dividend : , Divisor :
If when divided by , the remainder is , then find the value of .
and , find the remainder when is divided by .
Let and are the remainders when a polynomial and are divided by and respectively. If , find the value of .
If has a remainder when divided by , then
If has a remainder when divided by , then
To obtain the first term of the quotient divide the highest degree term of the dividend by the highest degree term of the _____.
Look at the polynomial $ \text{P}\left(x\right)$ below.
$ \text{P}\left(x\right)=2{x}^{3}-{x}^{2}-5x+11$
The number that should be added to $ \text{P}\left(x\right)$, to make the resulting polynomial completely divisible by $ x+1$ is _____.
The remainder of polynomial $ \text{Q}\left(x\right)={x}^{3}+m{x}^{2}-3x+7$ is $ -2$, when divided by $ (x+3)$.
Remainder obtained when $ \text{Q}\left(x\right)$ is divided by $ (x-4$) is _____.
Let $ \text{P}\left(x\right)$ be a polynomial and dividing $ \text{P}\left(x\right)$ by $ (x+1)$ leaves remainder 5.
Which of the following statements is true about remainder theorem?
Given, $ \text{P}\left(x\right)=(x+2)\times \text{Q}\left(x\right)$ where $ \text{Q}\left(x\right)={x}^{2}-\text{kx}-14$.
If dividing $ \text{P}\left(x\right)$by $ \left(x-2\right)$ leaves no remainder, then $ k$ is _____.
In the polynomial $ \text{P}\left(x\right)={x}^{3}+6{x}^{2}+\text{mx}-30,$both $ \left(x+5\right)$ and $ (x+3)$ are completely divisible.
The value of $ m$ in the polynomial $ \text{P}\left(x\right)$is _____.
The polynomial , when divided by , leaves a remainder . The value of is _____.
The polynomial , leaves the same remainder , when divided by or .
The value of is _____.
