Question 1 :
State whether the following statement is true or false.After dividing $$ (9x^{4}+3x^{3}y + 16x^{2}y^{2}) + 24xy^{3} + 32y^{4}$$ by $$ (3x^{2}+5xy + 4y^{2})$$ we get<br/>$$3x^{2}-4xy + 8y^{2}$$
Question 2 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$$\displaystyle x^2-\frac{1}{4x^2}; x-\frac{1}{2x}$$
Question 3 :
Is $$(3x^{2} + 5xy + 4y^{2})$$ a factor of $$ 9x^{4} + 3x^{3}y + 16x^{2} y^{2} + 24xy^{3}  + 32y^{4}$$?<br/>
Question 4 :
The product of the roots of the quadratic equation $$2x^{2}-8x+3=0$$ is
Question 5 :
State whether True or False.Divide : $$a^2 +7a + 12 $$ by $$  a + 4 $$, then the answer is $$a+3$$.<br/>
Question 7 :
If $$a\ne 2$$, which of the following is equal to $$\cfrac { b\left( { a }^{ 2 }-4 \right) }{ ab-2b } $$?
Question 8 :
Apply the division algorithm to find the remainder on dividing $$p(x) = x^4 -3x^2 + 4x + 5$$ by $$g(x)= x^2 +1 -x.$$
Question 10 :
State whether True or False.Divide: $$x^2 + 3x -54 $$ by $$ x-6 $$, then the answer is $$x+9$$.<br/>
Question 16 :
Find the expression which is equivalent to : $$\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $$?
Question 17 :
Factorise the expressions and divide them as directed.$$12xy(9x^2-  16y^2)\div  4xy(3x + 4y)$$
Question 18 :
If a polynomial $$p(x)$$ is divided by $$x - a$$ then remainder is<br/>
Question 19 :
Simplify:$$20(y + 4) (y^2 + 5y + 3) \div 5(y + 4)$$<br/>
Question 20 :
What is the remainder, when<br>$$(4{x^3} - 3{x^2} + 2x - 1)$$ is divided by (x+2)?<br>
Question 23 :
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 24 :
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 25 :
If $$\alpha$$ and $$\beta$$ are the zeroes of the polynomial $$4x^{2} + 3x + 7$$, then $$\dfrac{1}{\alpha }+\dfrac{1}{\beta }$$ is equal to:<br/>
Question 26 :
The degree of the remainder is always less than the degree of the divisor.
Question 27 :
Work out the following divisions.<br/>$$96abc(3a -12) (5b +30)\div  144(a-  4) (b+  6)$$<br/>
Question 29 :
What must be subtracted from $$4x^4 - 2x^3 - 6x^2 + x - 5$$, so that the result is exactly divisible by $$2x^2 + x - 1$$?
Question 31 :
If $${(5{x}^{2}+14x+2)}^{2}-{(4{x}^{2}-5x+7)}^{2}$$ is divided by $${x}^{2}+x+1$$, then the quotient $$q$$ and the remainder $$r$$ are given by:
Question 32 :
Find the product of roots if the quadratic equation $$ax^2+bx+c=0$$ has exactly one non-zero root.
Question 33 :
If the roots of the equation, $$ax^2+bx+c=0$$, are of the form $$\alpha / (\alpha -1)$$ and $$(\alpha +1)/\alpha$$, then the value of $$(a+b+c)^2$$ is
Question 35 :
Divide :$$\displaystyle \left[ { x }^{ 4 }-{ \left( y+z \right)  }^{ 4 }\right] \ by \left[{ x }^{ 2 }+{ \left( y+z \right)  }^{ 2 }\right]$$
Question 36 :
If $$\alpha$$ and $$\beta$$ are the zeros of the polynomial $$f(x)=5x^2+4x-9$$ then evaluate the following: $$\alpha^4-\beta^4$$<br/>
Question 37 :
If $$\alpha $$ and $$\beta$$ are the roots of a rational function $$\dfrac{2}{\alpha+1}-\dfrac{\alpha}{6}=0$$. What is the sum of $$\alpha+\beta$$?<br/>
Question 38 :
If $$3{p}^{2}=5p+2$$ and $$3{q}^{2}=5q+2$$, where $$p\ne q$$, then $$pq$$ is equal to
Question 39 :
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing $$f(x) =10x^4 +17x^3-62x^2+30x -3$$ by $$g(x) =2x^2-x+1$$