Test Details

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Polynomials

Feb 03, 4:00 PM

60 minutes

Feb 03, 5:00 PM

50.0 marks

MCQ

35 questions

Shiv Anand

Class Details

Maths

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Question Text

Question 2 :
Given that $x = 2$ is a solution of $x^3 - 7x + 6 = 0$. The other solutions are

Question 3 :
If x+2 is a factor of $ \displaystyle \left \{ \left ( x+1 \right )^{5}+(2x+k)^{3} \right \} $, then the value of 'k' is 

Question 4 :
Simplify: $(x - 3y - 5z)(x^2 + 9y^2 + 25z^2 + 3xy - 15yz + 5zx)$

Question 5 :
Find the expression which is equivalent to : $\displaystyle \frac { { x }^{ 3 }+{ x }^{ 2 } }{ { x }^{ 4 }+{ x }^{ 3 } } $?

Question 6 :
The product of $x^2y$ and $\cfrac{x}{y}$ is equal to the quotient obtained when $x^2$ is divided by ____.

Question 8 :
Let $r(x)$ be the remainder when the polynomial $x^{135}+x^{126}-x^{115}+x^{5}+1$ is divided by $x^{3}-x$. Then:

Question 9 :
If $p(x) = 2x^3-3x^2+4x-5$. Find the remainder when $p(x)$ is divided by , $x-1$

Question 10 :
If $(y - 3)$ is a factor of $y^{3} + 2y^{2} - 9y - 18$, then find the other two factors

Question 11 :
If $\dfrac {a^{2} + 2ab + b^{2}}{a^{2} - b^{2}} = 2a + 2b$, what is the value of $a - b$?

Question 12 :
Find the value of $k$, if $x-1$ is a factor of $p(x)$ in the following cases:$p(x)=kx^2-\sqrt 2x+1$

Question 13 :
Factorise : $(a - b)^3 + (b - c)^3 + (c - a)^3$

Question 14 :
If $a\, -\displaystyle \frac{1}{a}\, =\, 8$ and $a\, \neq\, 0$; find $a^{2}\, -\, \displaystyle \frac{1}{a^{2}}$

Question 16 :
The value of $k$ for which $x - k$ is a factor of $x^{3} - kx^{2} + 2x + k + 4$ is

Question 20 :
If $\dfrac{a}{b}$ + $\dfrac{b}{a}$ = 1, then $a^3$ + $b^3$ $=$

Question 21 :
Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x) q(x) + r(x) where deg r(x) = 0

Question 23 :
$\displaystyle\left( { 3x }^{ 2 }-x \right) \div \left( -x \right) $ is equal to

Question 24 :
When $x^{13} + 1$ is divided by $x - 1$, the remainder is

Question 25 :
If $x-2$ is a factor of $x^3 - 3x + 5a $ then find the value of $a.$

Question 28 :
If $a + b + c = 12$ and $a^{2}\, +\, b^{2}\, +\, c^{2}\, =\, 50$;  find $ab + bc + ca.$

Question 29 :
What is the value of $P$ for which $(a-2)$ is a factor of $a^2-5a+P$ ?

Question 31 :
If $2x^3 + 4x^2 + 2ax + b$ is exactly divisible by $x^2 - 1$, then the value of a and b respectively will be

Question 34 :
If $a + b + c = 0$, then $a^3 + b^3 + c^3$ is equal to

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