Question 1 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.<br/>
Question 3 :
If $\dfrac {a^{2} + 2ab + b^{2}}{a^{2} - b^{2}} = 2a + 2b$, what is the value of $a - b$?
Question 4 :
Divide the first expression by the second. Write the quotient and the remainder.<br/>$a^2-b^2 ; a-b$
Question 7 :
If (x -1) is a factor of polynomial f(x) but not of g(x), then it must be a factor of
Question 8 :
State whether the statement is True or False.Evaluate: $(6-xy)(6+xy)$ is equal to $36-x^2y^2$.<br/>
Question 9 :
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 11 :
On dividing $f(x)$ by a polynomial $x-1-x^2$, the quotient $q(x)$ and remainder $r(x)$ are $(x-2)$ and $3$ respectively. Then $f(x)$ is<br/>
Question 12 :
If $\displaystyle 2 \left ( x^{2} + 1 \right ) = 5x$, find $\displaystyle x - \dfrac{1}{x}$<br/>
Question 13 :
If the remainder, when polynomial $f(x)$ is divided by $x-1, x+1$, are $6, 8$ respectively, then the remainder, when $f(x)$ is divided by$ (x-1)(x+1)$ is :
Question 14 :
Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm. $x^3-3x+1, x^5-4x^3+x^2+3x+1$<br>
Question 15 :
For the remainder of the division of $x^{3}- 2x^{2}+ 3kx + 18$ by $x - 6$ to be equal to zero, k must be equal to<br>
Question 16 :
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 17 :
If ${x^2} - 3x + 2$ is a factor of $f(x) = {x^4} - p{x^2} + q$ ,then $(p,q) = $
Question 19 :
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 20 :
If $\displaystyle { n }^{ 3 }-{ n }^{ 2 }=n-1$, then which of the following can be the value of $ n$?