Question 2 :
The remainder obtained by dividing $x^{n} - \dfrac{a}{b}$ by $ax - b$ is<br/>
Question 3 :
The remainder when ${ n }^{ 2 }-6n-50(n\in N)$ is divided by $36$, is
Question 4 : <p>If $x^{51} + 51$ is divided by $x + 1$, then theremainder is</p>
Question 6 :
Workout the following divisions<br/>$54lmn (l + m) (m + n) (n + 1) \div 81mn (l + m) (n + l)$
Question 7 :
If ${ \left( x+\cfrac { 1 }{ x } \right) }^{ 2 }=9$, then the value of ${x}^{3}+\cfrac{1}{{x}^{3}}$ is-
Question 8 :
When $(x^3-2x^2+px-q)$ is divided by $(x^2-2x-3)$, the remainder is $(x-6)$. The values of $p$ and $q$ respectively are ____.
Question 10 :
For a polynomial $p\left( x \right) $, the value of $p\left( 3 \right) $ is $-2$. Which of the following must be true about $p\left( x \right) $?
Question 11 :
What should be added to $8x^4+14x^3-2x^2+7x-8$ so that the resulting polynomial is exactly divisible by $4x^2+3x-2$?<br/>
Question 13 :
For the remainder of the division of $x^{3}- 2x^{2}+ 3kx + 18$ by $x - 6$ to be equal to zero, k must be equal to<br>
Question 14 :
In the real number system, the equation<br>$\sqrt { x+3-4\sqrt { x-1 } } +\sqrt { x+8-6\sqrt { x-1 } } =1$
Question 15 :
If $\displaystyle \left ( x+2 \right )$ is a factor of the polynomial $\displaystyle f\left ( x \right )= x^{2}+ax+2b$ and $\displaystyle a+b=4$, then the value of $a$ and $b$ are-
Question 16 :
Obtain all the zeros of $3x^4+6x^3-2x^2-10x-5$, if two of its zeros are $\sqrt {\cfrac {5}{3}}$ and $-\sqrt {\cfrac {5}{3}}$<br/>
Question 18 :
If $2x+ky+z$ is a factor of $\displaystyle 9y^{2}-z^{2}-2xz+6xy $, then the value of k is equal to
Question 19 :
Find the values of $a$ and $b$ so that $x^4+x^3+8x^2+ax+b$ is divisible by $x^2+1$<br/>
Question 21 :
Let p(x) be a quadratic polynomial with constant term 1. Suppose $p(x)$ when divided by $x -1$ leaves remainder 2 andwhen divided by $x +1$ leaves remainder 4. Then the sum of the roots of $p(x) = 0$ is
Question 22 :
When $x^{13} + 1$ is divided by $x - 1$, the remainder is
Question 26 :
If $x + 2$ is factor of ${(x + 1)^{5} + (2x + K)^{3}}$, then the value of $'K'$ is<br/>
Question 27 :
State true or false:<br/>If $\displaystyle a + \dfrac{1}{a} = p$ and $\displaystyle a \neq 0$; then<br/>$\displaystyle a^{3} + \dfrac{1}{a^{3}} = p\left ( p^{2} - 3 \right )$<br/>
Question 29 :
The polynomials$\displaystyle ax^{3}+3x^{2}-3$ and$\displaystyle 2x^{3}-5x+a$ when divided by (x - 4) leaves remainder$\displaystyle R_{1}$ &$\displaystyle R_{2}$=0
Question 30 :
If $a + b + c = 0$, then $a^3 + b^3 + c^3$ is equal to
Question 31 :
If $2x^{3} + 4x^{2} + 2ax + b$ is exactly divisible by $x^{2} - 1$, then the value of $a$ and $b$, respectively will be<br/>
Question 33 :
The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their squares.
Question 34 :
If the remainder, when polynomial $f(x)$ is divided by $x-1, x+1$, are $6, 8$ respectively, then the remainder, when $f(x)$ is divided by$ (x-1)(x+1)$ is :
Question 36 :
If the expressions $ax^3+3x^2-3$ and $2x^3-5x+a$ on dividing by $x-4$ leave the same remainder, then the value of $a$ is :
Question 39 :
Find out whether or not the first polynomial is a factor of the second polynomial<br/>$x-3, x^3+4x^2-3x+5$
Question 40 :
Which among $-2$ and $1$  satisfy the equation $32 = 4x + 40$.<br/>
Question 43 :
Determine all the zeros of $x^4-x^3-8x^2+2x+12$ if two of its zeros are $\sqrt 2$ and $-\sqrt 2$<br>
Question 44 :
On dividing $f(x)$ by a polynomial $x-1-x^2$, the quotient $q(x)$ and remainder $r(x)$ are $(x-2)$ and $3$ respectively. Then $f(x)$ is<br/>
Question 45 :
If $(x-2)$ is a common factor of $x^3-4x^2+ax+b$ and $x^3-ax^2+bx+8$, then the values of $a$ and $b$ are respectively :
Question 46 :
The polynomial's $P(x)=k^2x^3+3x^2-3$ and $Q(x)=2x^3+4x+k$ when divided by $(x-1)$ leave the same remainder then the sum of all possible values of k is?
Question 47 :
$\root 3 \of a + \root 3 \of b + \root 3 \of c = 0\;{\text{then}}{\left( {a + b + c} \right)^3} $
Question 50 :
$12{\left( {x + 3y} \right)^4} - 6{\left( {x + 3y} \right)^3}$ is factorized then its simplified form is
