Question 1 :
The value of p for which $(x-2)$ is a factor of polynomial $x^4 - x^3 + 2x^2 - px +4$ is:<br/>
Question 3 :
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 4 :
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 5 :
$f(x)=2x^3-5x^2+ax+a$Given that $(x+2)$ is a factor of $f(x)$, find the value of the constant $a$.
Question 7 :
If the polynomial $x^3-x^2+x-1$ is divided by $x-1$, then the quotient is :
Question 8 :
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 9 :
State whether the following statement  is true or false.$(x-1)$ is a factor of ${x}^{3}-27{x}^{2}+8x$.
Question 11 :
The value of (a - b)(a$^2$ + ab + b$^2$) is
Question 12 :
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 16 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 17 :
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 18 :
What is the remainder when $\displaystyle 13x^{2}+22x-10$ is divided by $(x + 2)$ ?
Question 19 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in the following cases:$p(x)=kx^2-\sqrt 2x+1$<br/>
Question 23 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find :<br/>$\displaystyle  3\left ( a+b \right )^{2}-2\left ( a-b \right )^{2}$<br/>
Question 25 :
If $x-3$ is a factor of $x^3+3x^2+3x+p$, then find the value of $p$.
Question 27 :
If $ a^2+b^2=29 $ and $ ab=10 $, then find $ a-b $. 
Question 28 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.<br/>
Question 29 :
Use the factor theorem and state whether $g(x)$ is a factor of $p(x)$ in the following case. State True Or False:$p(x)=x^3-4x^2+x+6; \ g(x)=x-3$<br/>
Question 31 :
If $\left (x + \dfrac {1}{x}\right ) = 2\sqrt {3}$, then the value of $\left (x^{3} + \dfrac {1}{x^{3}}\right )$ is
Question 32 :
Simplify: $(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$
Question 33 :
Factorise : $(a - b)^3 + (b - c)^3 + (c - a)^3$
Question 36 :
If $(x -2)$ is a factor of $x^2 + 4x -2k$, then the value of k is
Question 38 :
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 39 :
Use the identity $(x + a) (x + b) = x^2 + (a + b) x + ab$ to find the following products.$(xyz +4) (xyz +2)$
Question 40 :
Find out whether or not the first polynomial is a factor of the second polynomial:$4a-1, 12a^2-7a-2$
Question 41 :
State whether the statement is True or False.The square of $(2x+\dfrac{1}{x}+1) $ is equal to $4x^2+\dfrac{1}{x^2}+5+\dfrac{2}{x}+4x $.<br/>
Question 42 :
If ${ x }^{ 3 }+ax-28$ is exactly divisible by $x-4$, then the value of $a$ is
Question 45 :
The value of $\displaystyle\left (5^{\cfrac {1}{2}} + 3^{\cfrac {1}{2}}\right ) \left (5^{\cfrac {1}{2}} - 3^{\cfrac {1}{2}}\right )$ is
Question 46 :
The degree of the remainder is always less than the degree of the divisor.
Question 47 :
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 48 :
If the polynomial $3x^4-4x^3-3x-1$ is divided by $x-1$, then the remainder is :
Question 49 :
State whether the statement is True or False.$(3x-2y)^3 $ is equal to $27x^3-54x^2y+36xy^2-8y^3$.<br/>
Question 50 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?
