Question 1 :
State true or false: $(x + a) (x + b) = x^2 + (a + b)x + ab$
Question 2 :
What is $ x^3 + y^3 + z^3 – 3xyz$ equal to?
Question 4 :
State true or false: 7 + 3x is a factor of $3x^3 + 7x$.
Question 5 :
Possible expressions for the dimension of cuboid having volume :$12ky^2+ 8ky – 20k$ are-
Question 6 :
The zero of the polynomial p(x) = x + 5 is-
Question 9 :
Does $x^4 + 3x^3 + 3x^2 + x + 1$ has x+1 as a factor -
Question 12 :
Factors of $4x^2+ y^2+ z^2– 4xy – 2yz + 4xz$ are-
Question 24 :
Is $x=-1,2$ a zero of $p(x) = (x + 1) (x – 2)$?
Question 26 :
Is $x+1$ a factor of $p(x) = 2x^3 + x^2 – 2x – 1$ -
Question 31 :
The remainder when $x^3 + 3x^2 + 3x + 1$ is divided by x + 1 is-
Question 33 :
The remainder when $x^3 + 3x^2 + 3x + 1$ is divided by 5 + 2x is-
Question 35 :
What is the value of p(2) for the polynomial $p(x)=x^3$ ?
Question 42 :
What is the value of p(1) for the polynomial $p(x) = (x – 1) (x + 1)$ ?
Question 43 :
If x – 1 is a factor of $p(x) = 2x^2+ kx +\sqrt{2}$ , k is-
Question 45 :
What is the value of p(1) for the polynomial $p(x)=x^3$ ?
Question 46 :
Factors of $2x^2 + y^2 + 8z^2 – 2\sqrt{2}xy + 4\sqrt{2}yz – 8xz$ are-
Question 48 :
Is $x – 3$ a factor of $p(x) = x^3– 4x^2 + x + 6$-
Question 50 :
If x – 1 is a factor of $p(x) = kx^2– 3x + k$ , k is-
Question 51 :
If $(x -2)$ is one factor of $x^2 +ax-6 = 0$ and  $ x^2 -9x + b= 0 $ then a + b = ____
Question 52 :
The value of $k$ for which $x - k$ is a factor of $x^{3} - kx^{2} + 2x + k + 4$ is<br/>
Question 54 :
If $\displaystyle a + \dfrac{1}{a} = m$ and $\displaystyle a \neq 0$; find in terms of $\displaystyle 'm'$ ; the value of: $\displaystyle a - \dfrac{1}{a}$
Question 55 :
The polynomials $ax^3 + 3x^2 - 13$ and $ 2x^3 -5x+a$ are divided by $x+2$ if the remainder in each case is the same, find the value of $a$.<br/>
Question 56 :
If one factor of the expression $x^{3} + 7kx^{2}-4kx+12$ is $(x+3)$, then the value of $k$ is<br/>
Question 57 :
Using factor theorem to determine whether (x-2) is a factor of$x^3-3x^2+4x+4$.
Question 58 :
The value of$ \displaystyle \frac{(1.5)^{2}+(4.7)^{3}+(3.8)^{3}-3\times 1.5\times 4.7\times 3.8}{(1.5)^{2}+(4.7)^{2}+(3.8)^{2}-1.5\times 4.7-4.7\times 3.8-1.5\times 3.8} $
Question 59 :
Given $\boxed { \begin{matrix} A \\ B \end{matrix} } ={A}^{2}+{B}^{2}+2AB$, what is $A+B$, if $\boxed { \begin{matrix} A \\ B \end{matrix} } =9$?
Question 60 :
If $P=\dfrac {{x}^{2}-36}{{x}^{2}-49}$ and $Q=\dfrac {x+6}{x+7}$ then the value of $\dfrac {P}{Q}$ is:
Question 61 :
If on division of a polynomial p (x) by a polynomial g (x), the quotient is zero, what is the relation between the degrees of p (x) and g (x) ?<br/>
Question 62 :
If the quotient $=\, 3x^2\, -\, 2x\, +\, 1,$ remainder $= 2x - 5$ and the divisor $= x + 2$, then the dividend is
Question 63 :
The number of times 99 is subtracted from 1111 so that the remainder is less than 99, is :<br>
Question 64 :
If $ a^2+b^2=29 $ and $ ab=10 $, then find $ a-b $. 
Question 65 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 66 :
By Remainder Theorem find the remainder, when $ p(x)$ is divided by $g(x)$, where$p(x) = 4x^3 -12x^2 + 14x -3, g(x) = 2x -1$
Question 67 :
State whether the statement is True or False.Evaluate: $(4x^2-5y^2)(4x^2+5y^2)$ is equal to $16x^4-25y^4$.<br/>
Question 70 :
If the polynomials $2x^{3} + ax^{2} + 3x - 5$ and $x^{3} + x^{2} - 4x + a$ leave the same remainder when divided by $x - 2$, find the value of $a$
Question 72 :
If $x+y -z = 4$ and $x^2+y^2+ z^2=50$, find the value of $xy -yz-zx$
Question 73 :
If $x\ne -5$ , then the expression $\cfrac{3x}{x+5}\div \cfrac {6}{4x+20}$ can be simplified to
Question 74 :
Factors of $\left (x^{2} + \dfrac {x}{6} - \dfrac {1}{6}\right )$ are
Question 75 :
Let $r(x)$ be the remainder when the polynomial $x^{135}+x^{126}-x^{115}+x^{5}+1$ is divided by $x^{3}-x$. Then:
Question 77 :
What is $\dfrac {x^{2} - 3x + 2}{x^{2} - 5x + 6} \div \dfrac {x^{2} - 5x + 4}{x^{2} - 7x + 12}$ equal to
Question 79 :
<b></b>If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a+b $. 
Question 80 :
State whether the statement is True or False.Evaluate: $(6-xy)(6+xy)$ is equal to $36-x^2y^2$.<br/>
Question 81 :
State whether the statement is True or False.Evaluate: $(7x+\dfrac{2}{3}y)(7x-\dfrac{2}{3}y)$ is equal to $49x^2-\dfrac{4}{9}y^2$.<br/>
Question 83 :
The remainder when $x^{3} - 6x^{2} + 11x - 6$ is divided by $x + 2$ is<br>
Question 85 :
The remainder when $x^{6} - 3x^{5} + 2x^{2} + 8$ is divided by $x - 3$ is<br>
Question 87 :
If $(x -2)$ is a factor of $x^2 + 4x -2k$, then the value of k is
Question 88 :
What must be added to $x^3-3x^2-12x + 19$, so that the result is exactly divisible by $x^2 + x-6$?
Question 89 :
The product of $x^2y$ and $\cfrac{x}{y}$ is equal to the quotient obtained when $x^2$ is divided by ____.<br/>
Question 90 :
Let $f(x)$ be polynomial in $x$ of degree not less than $1$ and $'a'$ be a real number. If $f(x)$ is divided by $(x-a)$, then the remainder is $f(a)$. If $(x-a)$ is a factor of $f(x)$, then $f(a) = 0$. Find the remainder of $x^4+x^3-x^2+2x+3$ when divided by $x-3.$
Question 91 :
If $\displaystyle \dfrac{x^{2} + 1}{x} = 3\dfrac{1}{3}$ and $\displaystyle x > 1$; find the value of  $\displaystyle x - \dfrac{1}{x}$
Question 93 :
If $(x-1)$ is a factor of $x^2 + 2x - k$, then find $k$.
Question 94 :
If the polynomial $x^3-x^2+x-1$ is divided by $x-1$, then the quotient is :
Question 95 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in the following cases:$p(x)=kx^2-3x+k$<br/>
Question 96 :
If x -a is a factor of $x^3 -3x^2a + 2a^2x + b$, then the value of b is
Question 97 :
What is the remainder when $\displaystyle 13x^{2}+22x-10$ is divided by $(x + 2)$ ?
Question 98 :
If on dividing a non-zero polynomial $p(x)$ by a polynomial $g (x)$, the remainder is zero, what is the relation between the degrees of $p(x)$ and $g (x)$?<br/>
Question 100 :
If x+2 is a factor of $ \displaystyle \left \{ \left ( x+1 \right )^{5}+(2x+k)^{3} \right \} $, then the value of 'k' is 
Question 101 :
Workout the following divisions<br/>$54lmn (l + m) (m + n) (n + 1) \div 81mn (l + m) (n + l)$
Question 102 :
Obtain all the zeros of $2x^4+5x^3-8x^2-17x-6$ if three of its zeros are $-1, -3, 2$.<br/>
Question 103 :
A polynomial when divided by $\displaystyle \left ( x-6 \right )$ gives a quotient $\displaystyle x^{2}+2x-13$ and leaves a remainder $-8$. Then polynomial is
Question 104 :
How many pairs of natural numbers are there so that difference of the square of the first tois 60 ?<br>(Note : If (a,b) is a pair satisfying , we will not consider (b,a) as a pair)
Question 105 :
If $x - \dfrac{1}{x} = 5$, then $x^{3} - \dfrac{1}{x^{3}}$ equals<br/>
Question 106 :
If $\sqrt {x} + \dfrac {1}{\sqrt {x}} =3,$ find the value of $x^{2}+ \dfrac {1}{x^{2}}$  :
Question 107 :
If $a + b + c = 12$ and $a^{2}\, +\, b^{2}\, +\, c^{2}\, =\, 50$;  find<br/>$ab + bc + ca.$
Question 109 :
Factorise : ${ (ax+by) }^{ 2 }+{ (2bx-2ay) }^{ 2 }-6abxy$
Question 111 :
If $3x^{3} - 2x^{2}y - 13xy^{2} + 10y^{3}$ is divided by $x - 2y$, then what is the remainder?
Question 112 :
If $x + y = 5$ and $x^2 + y^2 = 111$. then value of $x^3 + y^3$ is
Question 113 :
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 114 :
If $3x-7y = 10$ and $xy = -1$, then the value of $9x^2\, +\, 49y^2$ is equal to
Question 118 :
Using the reals $a_n; \hspace {2mm} (n=1,2,...,5)$, if $l,m,n \in \{1,2,3,4,5\}$ $m < n$.
Question 120 :
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 121 :
On dividing $x^3-3x^2+x+2$ by a polynomial $g(x)$, the quotient and remainder were $(x-2)$ and $(-2x+4)$, respectively. Find $g(x)$.<br/>
Question 125 :
If both $x - 2$ and  $x - \dfrac {1}{2}$ are factors of $px^2 + 5x + r$. Which of the conditions hold true?
Question 126 :
If $f(x) = 16x^2+51x+35$, then one of the factors of $f(x)$ is :
Question 127 :
The value of $p$ for which the polynomial $ 2x^4 + 3x^3 + 2px^2 + 3x + 6$ is exactly divisible by $ (x + 2) $is  
Question 128 :
A number which when divided by $10$ leaves a remainder of $9$, when divided by $9$ leaves remainder of $8$, and when divided by $8$ leaves a remainder of $7$, is
Question 129 :
The value of $k$ for which $(x - 1)$ is a factor of $x^{3} - kx^{2} + 11x - 6$ is<br/>
Question 130 :
If $x + 2$ is a factor of $x^{2} + mx + 14$, then $m =$
Question 131 :
$\displaystyle \left ( 1-a \right )\left ( 1+a+a^{2} \right )+\left ( 1+a \right )\left ( 1-a+a^{2} \right )$ is equal to
Question 132 :
If$\displaystyle \left ( a+b+c \right )^{2}=3\left ( ab+bc+ca \right )$, then which one of the following is true?
Question 135 :
The polynomial $\displaystyle p(x)=2x^{4}-x^{3}-7x^{2}+ax+b$ is divisible by $\displaystyle x^{2}-2x-3$ for certain values of $a$ and $b$. The value of $(a + b)$ is:
Question 141 :
If $\displaystyle \sum _{ a,b,c }^{  }{ a=0 } $ then the value of $\displaystyle \sum _{ a,b,c }^{  }{ { a }^{ 3 }-abc } $ is
Question 142 :
$\displaystyle \left ( x \right )^{n}+\left ( a \right )^{n}$ is divisible (remainder 0) by x + a, then n can be
Question 143 :
If $ax^2+2a^2x+b^3$ is divisible by $x+a$, then what is the relation between $'a'$ and $'b'$ is possible?
Question 146 :
If $\displaystyle f\left ( x \right )=x^{4}-2x^{3}+3x^{2}-ax+b $ is a polynomial such that when it is divide by $(x - 1)$ and $(x + 1)$ the remainders are $5$ and $19$ respectively the remainder when $f(x)$ is divisible by $(x - 2)$ is 
Question 148 :
If ${ \left( x+\cfrac { 1 }{ x } \right) }^{ 2 }=9$, then the value of ${x}^{3}+\cfrac{1}{{x}^{3}}$ is-
Question 149 :
If $x + 1$ is a factor of the polynomial $2x^2 + kx,$ then the value of $k$ is
Question 150 :
Polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and deg $r(x)=0$, are<br/>
Question 153 :
If $ax^{3}+ bx^{2}+ c x + d$ is divided by $x - 2$, then the remainder is equal<br>
Question 154 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to
Question 155 :
If $8a-64b-c=24\sqrt [ 3 ]{ abc } $, where a, b, $c\neq 0$, then which of the following can be true ?
Question 156 :
When $2f^3 + 3f^2 - 1$ is divided by $f+2$, find the remainder.<br/>
Question 157 :
The value of $x+y+z$ if ${x}^{2}+{y}^{2}+{z}^{2} = 18$ and $xy + yz + zx = 9$ is
Question 159 :
If a remainder of $4$ is obtained when $x^{3} + 2x^{2} - x - k$ is divided by $x - 2$, find the value of $k$.
Question 160 :
If the roots of ${x^4} + q{x^2} + kx + 225 = 0$ are in arithmetic progression, then the value of q is
Question 161 :
Total number of polynomials of the form ${ x }^{ 3 }+a{ x }^{ 2 }+bx+c$ that are divisible by ${ x }^{ 2 }+1$, where $a,b,c\in \left\{ 1,2,3,......10 \right\} $ is equal to
Question 162 :
The equationd $x^{x^{x^{+}}} = 2$ is satisfied when $x$ is equal to
Question 163 :
Square root of $\dfrac {x^{2}}{y^{2}} + \dfrac {y^{2}}{4x^{2}} - \dfrac {x}{y} + \dfrac {y}{2x} - \dfrac {3}{4}$ is $\dfrac {x}{y} - \dfrac {1}{2} - \dfrac {y}{2x}$
Question 164 :
Assertion: Let $\displaystyle f\left ( x \right )=6x^{4}+5x^{3}-38x^{2}+5x+6 $ then all four roots of $\displaystyle f\left ( x \right )=0 $ are real & distinct out of which two are positive & two are negative.
Reason: $\displaystyle f\left ( x \right ) $ has two changes in sign in given order as well as when $x$ is replaced by $-x$.
Question 165 :
When a number P is divided by 4 it leaves remainder 3. If twice of the number P is divided by the same divisor 4, then what will be the remainder?
Question 167 :
If $\displaystyle { n }^{ 3 }-{ n }^{ 2 }=n-1$, then which of the following can be the value of $ n$?
Question 168 :
Which of the following is a factor of the polynomial $-2{x}^{2}+7x-6$?
Question 169 :
Number of real solutions of $\sqrt { 2 x - 4 } - \sqrt { x + 5 } = 1$...
Question 170 :
Which of the following should be added to $\displaystyle 9x^{3}+6x^{2}+x+2$ so that the sum is divisible by $(3x + 1)$?
Question 171 :
Find the value of the reminder obtained when $6x^4 + 5x^3 - 2x + 8$ is divided by $x-\dfrac{1}{2}$.
Question 172 :
Find the factor of the polynomial $P(x)= \left (12x^4+13x^3-35x^2-16x+20 \right )$ .<br/>
Question 173 :
Let p(x) be a quadratic polynomial such that $p(0)=1$. If p(x) leaves remainder $4$ when divided by $x-1$ and it leaves remainder $6$ when divided by $x+1$; then which one is correct?
Question 174 :
Let $f(x)=x^6-2x^5+x^3+x^2-x-1$ and $g(x)=x^4-x^3-x^2-1$ be two polynomials. Let $a,b,c$ and $d$ be the roots of $g(x)=0$. Then the value of $f(a)+f(b)+f(c)+f(d)$ is
Question 175 :
If n is an integer, what is the remainder when $5x^{2n + 1}- 10x^{2n} + 3x^{2n-1} + 5$ is divided by x + 1?
Question 176 :
Let P be a non zero polynomial such that $P(1 + x) = P(1 - x)$ for all real x, and $P(1) = 0$. Let m be the largest integer such that $(x - 1)^m$ divides $P(x)$ for all such $P(x)$. Then m equals
Question 177 :
When a positive integer $y$ is divided by $47,$ the remainder is $11$. Therefore, when $\displaystyle y^{2}$ is divided by $47$, the remainder will be 
Question 178 :
If ${x^2} - 3x + 2$ is a factor of $f(x) = {x^4} - p{x^2} + q$ ,then $(p,q) = $
Question 179 :
If $\displaystyle { \left( n+1 \right)  }^{ 3 }-{ n }^{ 3 }=-n$ , then which of the following can be the value of $n$ ?
Question 181 :
If$\displaystyle x=a\left ( b-c \right );y=b\left ( c-a \right );z=c\left ( a-b \right )$ then$\displaystyle \left ( \frac{x}{a} \right )^{3}+\left ( \frac{y}{b} \right )^{3}+\left ( \frac{z}{c} \right )^{3}$ is equal to
Question 184 :
Simplify: $\displaystyle \frac { 49\left( { x }^{ 4 }-2{ x }^{ 3 }-15{ x }^{ 2 } \right)  }{ 14x\left( x-5 \right)  } $
Question 186 :
Which of the following is the remainder when $z\left({5z}^{2}-80\right)$ is divided by $5z\left(z-4\right)$:
Question 187 :
If $\displaystyle { \left( n+1 \right)  }^{ 3 }-{ \left( n-1 \right)  }^{ 3 }=n+2$, then which of the following can be the value of $n$ ?<br/>
Question 189 :
If $(x - 2)$ and $(x - 3)$ are two factors of $\displaystyle x^{3}+ax+b$, then find the remainder when $\displaystyle x^{3}+ax+b$ is divided by $x - 5$.
Question 190 :
Divide $\displaystyle 10{ a }^{ 2 }{ b }^{ 2 }\left( 5x-25 \right)$ by $15ab\left( x-5 \right) $
