Question Text
Question 1 :
If quotient = $$3x^2\, -\, 2x\, +\, 1$$, remainder = $$2x - 5$$ and divisor  = $$x + 2$$, then the dividend is:
Question 2 :
Find the expression which is equivalent to : $$\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $$?
Question 3 :
Factorise the expressions and divide them as directed.$$39y^3(50y^2 -98) \div 26y^2(5y + 7)$$
Question 4 :
If $$(x-1)$$ is a factor of $$x^2 + 2x - k$$, then find $$k$$.
Question 5 :
State whether the statement is True or False.Evaluate: $$(6-xy)(6+xy)$$ is equal to $$36-x^2y^2$$.<br/>
Question 6 :
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 8 :
Find the value of $$k$$, if $$x-1$$ is a factor of $$p(x)$$ in the following cases:$$p(x)=kx^2-3x+k$$<br/>
Question 9 :
If $$\left (x + \dfrac {1}{x}\right ) = 2\sqrt {3}$$, then the value of $$\left (x^{3} + \dfrac {1}{x^{3}}\right )$$ is
Question 10 :
Simplify: $$(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$$