Remainder and Factor Theorem
Remainder and Factor Theorem: Overview
This topic covers concepts such as Quotient-Remainder Theorem, Remainder Theorem, Factor Theorem and Factor Theorem as Particular Case of Remainder Theorem.
Important Questions on Remainder and Factor Theorem
If has a remainder when divided by , then
If is a factor of , then find the value of .
is a factor of . Which of the following is true?
If has a remainder when divided by , then
The polynomial cannot be factored into a product of the first-degree polynomial.
If is a factor of the polynomial , then the value of is
If is a factor of the polynomial , then the value of is:
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 _____.
The polynomial $ \text{P}\left(x\right)={x}^{3}-2{x}^{2}+3x+7$, when divided by$ (x-2)$, leaves a remainder _____.
Consider the polynomial$ \text{P}\left(x\right)={x}^{4}+{x}^{3}-4{x}^{2}-2\text{x}+4$.
Two of its factors are $ \left(x-\sqrt{2}\right)$ and $ \left(x+\sqrt{2}\right)$
What are the other two factors of $ \text{P}\left(x\right)$?
$ \text{P}\left(x\right)=(x-1)(x-2)(x-3)$
Which of the following is/are factor(s) of the polynomial, $ \text{P}\left(x\right)$?
(i) $ (x-1)$
(ii) $ (x+1)$
(iii) $ ({x}^{2}-3x+2)$
(iv) $ ({x}^{2}-5x+6)$
(v) $ ({x}^{2}-1)$
Which of the following statements is true about the polynomial, $ \text{P}\left(x\right)$ according to factor theorem?
Two factors of a polynomial are and
The third factor of is _____.
Which of the following is a factor of the polynomial $ \text{P}\left(x\right)=(-x-2)(x+3)$?
