Question 1 :
The value of $k$ for which $x - k$ is a factor of $x^{3} - kx^{2} + 2x + k + 4$ is<br/>
Question 2 :
State True or False, if the following are zeros of the polynomial, indicated against them:<br/>$p(x)=3x+1, \ x=-\dfrac {1}{3}$<br/>
Question 3 :
If $\displaystyle x \neq 0$, $\displaystyle x + \dfrac{1}{2x} = p$ and $\displaystyle x - \dfrac{1}{2x} = q$; find a relation between $\displaystyle p$ and $\displaystyle q$.
Question 4 :
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 5 :
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 7 :
Find the zero of the polynomial $p(x)=cx+d, \ c\neq 0$, \ c, d are real numbers<br/>
Question 8 :
State whether True or False, if the following are zeros of the polynomial, indicated against them:$p(x)=lx+m, \ x=-\dfrac {m}{l}$<br/>
Question 9 :
State whether the statement is True or False.Evaluate: $(6-5xy)(6+5xy)$ is equal to $36-25x^2y^2$.
Question 10 :
If the quotient of $\displaystyle x^4 - 11x^3 + 44x^2 - 76x +48$. When divided by $(x^2 - 7x +12)$ is $Ax^2 + Bx + C$, then the descending order of A, B, C is
Question 12 :
If $\displaystyle  a^{2}+b^{2}=13 \ and \ ab=6 $ find :<br/>$\displaystyle  a^{2}-b^{2}$<br/>
Question 14 :
Find the Quotient and the Remainder when the first polynomial is divided by the second.$-6x^4 + 5x^2 + 111$ by $2x^2+1$
Question 15 :
If $(x -2)$ is one factor of $x^2 +ax-6 = 0$ and  $ x^2 -9x + b= 0 $ then a + b = ____
Question 16 :
If $kx^3 + 9x^2+4x -10 $ divided by $x+3$ leaves a remainder $5$, then the value of $k$ will be 
Question 17 :
If one factor of the expression $x^{3} + 7kx^{2}-4kx+12$ is $(x+3)$, then the value of $k$ is<br/>
Question 20 :
<b></b>If $ a^2+b^2=10 $ and $ ab=3 $, then find $ a+b $. 
Question 21 :
State true or false:<br/>If $\displaystyle a + 2b + c = 0$; then <br/>$\displaystyle a^{3} + 8b^{3} + c^{3} = 6abc$<br/>
Question 22 :
Verify whether the following are zeros of the polynomial indicated against them:<br/>$s(x)=x^2, \ x=0, 1$<br/>
Question 24 :
If quotient = $3x^2\, -\, 2x\, +\, 1$, remainder = $2x - 5$ and divisor  = $x + 2$, then the dividend is:
Question 25 :
Find the remainder when $x^{3} + 3x^{2} + 3x + 1$ is divided by $x - \dfrac {1}{2}$.
Question 26 :
The roots of $x(x^2 + 8x + 16)(4 - x ) = 0$ are
Question 28 :
State whether the statement is True or False.Expand: $(2a+b)^2 $ is equal to $4a^2+4ab+b^2$.<br/>
Question 29 :
If $x+y -z = 4$ and $x^2+y^2+ z^2=50$, find the value of $xy -yz-zx$
Question 31 :
The remainder when the polynomial $p(x) = x^{100} -x^{97} + x^3$ is divided by $x + 1$ is
Question 32 :
Verify whether the following are zeros of the polynomial indicated against them:$g(x)=5x^2+7x, \ x=0, -\dfrac {7}{5}$<br/>
Question 33 :
Verify whether the following are zeros of the polynomial indicated against them:<br/>
Question 34 :
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 35 :
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 37 :
State whether the given statement is true or false:Zero of $q(x) = 2x - 7$ is  $x=\cfrac{7}{2}$<br/>
Question 40 :
Which of the following polynomials has $- 3$ as a zero ?<br>
Question 41 :
Without actually calculating the cubes, find the value of each of the following:$(28)^3+(-15)^3+(-13)^3$<br/>
Question 42 :
Can $(x - 1)$ be the remainder on division of a polynomial $p(x)$ by $2x + 3$? <br/>
Question 43 :
Using factor theorem to determine whether (x-2) is a factor of$x^3-3x^2+4x+4$.
Question 47 :
Divide:$\left ( 15y^{4}- 16y^{3} + 9y^{2} - \cfrac{1}{3}y - \cfrac{50}{9} \right )$ by $(3y-2)$Answer: $5y^{3} + 2y^{2} - \cfrac{13}{3}y + \cfrac{25}{9}$
Question 49 :
If ${ x }^{ 3 }+ax-28$ is exactly divisible by $x-4$, then the value of $a$ is