Question Text
Question 1 :
One factor of $x^4 + x^2-20$ is $x^2+ 5$. The other factor is
Question 2 :
If $p(x) = x^3-3x^2+6x-4$ and $p\left (\dfrac{\sqrt{3}}{2}\right) = 0$ then by factor theorem the corresponding factor of $p(x)$ is <br/>
Question 5 :
State whether the statement is True or False.Evaluate: $(2a+3)(2a-3)(4a^2+9)$ is equal to $16a^4-81$.<br/>
Question 6 :
If $x + y = 5, x^3+ y^3 = 35$, then $x -y$ is equal to
Question 7 :
On dividing a number by $56$, we get $29$ as remainder. On dividing the same number by $8$, what will be the remainder ?
Question 8 :
Determine all the zeros of $4x^3+5x^2-180x-225$ if one of its zeros is $-\cfrac {5}{4}$.<br/>
Question 9 :
$\displaystyle\left( { 3x }^{ 2 }-x \right) \div \left( -x \right) $ is equal to
Question 10 :
Given $ax^2+bx+c$ is a quadratic polynomial in x and leaves remainders 6, 11 and 18 respectively when divided by $(x+1), (x+2) and (x+3)$. Find the value of $a+b+c.$<br/>
Question 11 :
If $x - 3$ is a factor of $x^{2} - ax - 15$, then $a =$
Question 12 :
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 13 :
$\displaystyle \frac{x^{-1}}{x^{-1} + y^{-1}} + \frac{x^{-1}}{x^{-1} - y^{-1}}$ is equal to