Question 1 :
Divide the given polynomial by the given monomial:<br/><br/>$\left(\dfrac{2}{3} a^2 b^2 c^2 + \dfrac{4}{3} ab^2 c^2 \right ) \div \dfrac{1}{2} abc$
Question 5 :
When ${ x }^{ 2 }-2x+k$ divided the polynomial ${ x }^{ 2 }-{ 6x }^{ 3 }+16{ x }^{ 2 }-25x+10$ the reminder is (x+a), the value of is
Question 6 :
There are $x^{4} + 57x + 15$ pens to be distributed in a class of $x^{2} + 4x + 2$ students. Each student should get the minimum possible number of pens. Find the number of pens received by each student and the number of pens left undistributed $(x\epsilon N)$.
Question 7 :
If the polynomial $(x + 1)^{2015} - x^{2015} - 1$ is divided by $(x + x^2 + x^3)$, then the remainder is
Question 8 :
Choose the correct answer from the alternatives given :<br>Whenthe polynomial $(6x^4 \, + \, 8x^3 \, + \, 17x^2 \, + \, 21x \, + \, 7)$ is divided by $(3x^2 \,+ \, 4x \, + \, 1)$ , the remainder is (ax + b). Therefore,
Question 10 :
(64x$^3$ + y$^3$) $\div$ (16x$^2$ - 4xy + y$^2$) is equal to
Question 12 :
Divide $\displaystyle 4{ x }^{ 2 }{ y }^{ 2 }\left( 6x-24 \right) \div 4xy\left( x-4 \right) $
Question 13 :
Simplify: $\displaystyle \frac { 20xyz\left( 4x+5y+6z \right)  }{ xz\left( 40x+50y+60z \right)}$
Question 16 :
Simplify: $\displaystyle \frac { 36ab\left( a+2 \right) \left( a+3 \right)  }{ 12a\left( a+3 \right)  } $
Question 17 :
Divide $\displaystyle ( 36{ x }^{ 2 }-4 )$ by $\left( 6x-2 \right) $
Question 19 :
The value of $\displaystyle \frac { 28xy\left( y-5 \right) \left( y+4 \right)  }{ 14y\left( y-5 \right)}$ is 
Question 20 :
Divide the following and write your answer in lowest terms: $\dfrac{x}{x+1}\div \dfrac{x^2}{x^2-1}$
Question 21 :
Evaluate :$\displaystyle \frac { 60pqr\left( { p }^{ 2 }+{ q }^{ 2 } \right) \left( { q }^{ 2 }+{ r }^{ 2 } \right) \left( { r }^{ 2 }+{ p }^{ 2 } \right) }{ 30pq\left( { p }^{ 2 }+{ q }^{ 2 } \right) \left( { r }^{ 2 }+{ p }^{ 2 } \right) }$
Question 22 :
Divide $\displaystyle 8\left( 3x+4 \right) \left( 8x+9 \right) $ by $\displaystyle \left( 3x+4 \right) $
Question 23 :
If $\cfrac{a}{b}=\cfrac{c}{d}=\cfrac{e}{f}$ and $\cfrac { 2{ a }^{ 4 }{ b }^{ 2 }+3{ a }^{ 2 }{ c }^{ 2 }-5{ e }^{ 4 }f }{ 2{ b }^{ 6 }+3{ b }^{ 2 }{ d }^{ 2 }-5{ f }^{ 5 } } ={ \left( \cfrac { a }{ b } \right) }^{ n }$ then the value if $n$ is
Question 26 :
On dividing $x^3-3x^2+x+2$ by polynomial $g(x)$, the quotient and remainder were $x -2$ and $4 - 2x$ respectively, then $g(x)$ is<br/>
Question 29 :
What must be added to $f(x)=4x^4+2x^3+2x^2+x-1$ so that the resulting polynomial is divisible by $g(x)=x^2+2x-3$<br>
Question 30 :
Find the polynomial which when divided by $3x + 4$, equals $2x^{2} + 5x - 3$ with a remainder of $3$
Question 36 :
If $\displaystyle \left ( 14x^{2}+13x-15 \right )$ is divided by $\displaystyle \left ( 7x-4 \right )$, the degree of the remainder is
Question 37 :
Simplify: $\displaystyle 18xy\left( 16{ x }^{ 2 }-25{ y }^{ 2 } \right) \div 3xy\left( 4x+5y \right) $
Question 38 :
Divide :$\displaystyle \left[ { x }^{ 4 }-{ \left( y+z \right)  }^{ 4 }\right] \ by \left[{ x }^{ 2 }+{ \left( y+z \right)  }^{ 2 }\right]$
Question 40 :
Evaluate: $\displaystyle \frac { x\left( 8{ x }^{ 2 }-32 \right)  }{ 8x\left( x-4 \right)  } $
Question 41 :
The area of a rectangle is $\displaystyle 12y^{4}+28y^{3}-5y^{2}$. If its length is $\displaystyle 6y^{3}-y^{2}$, then its width is
Question 42 :
Divide the following and write your answer in lowest terms: $\dfrac{x^2-4x-5}{x^2-25}\div \dfrac{x^2-3x-10}{x^2+7x+10}$
Question 45 :
Divide the following and write your answer in lowest terms: $\dfrac{x^2+11x+28}{x^2-4x-77}\div \dfrac {x^2+7x+12}{x^2-2x-15}$
Question 46 :
Divide the following and write your answer in lowest terms: $\dfrac{x^2-36}{x^2-49}\div \dfrac{x+6}{x+7}$
Question 47 :
Workout the following divisions<br/>$54lmn (l + m) (m + n) (n + 1) \div 81mn (l + m) (n + l)$
Question 48 :
Divide the following and write your answer in lowest terms: $\dfrac{2x^2+5x-3}{2x^2+9x+9}\div \dfrac{2x^2+x-1}{2x^2+x-3}$
Question 49 :
Evaluate: $96 abc (3a -12)(5b -30) \div 144 (a -4) (b -6)$
Question 50 :
Divide the following and write your answer in lowest terms: $\dfrac{3x^2-x-4}{9x^2-16}\div \dfrac {4x^2-4}{3x^2-2x-1}$
