Question Text
Question 1 :
The coefficient of $x$ in the expansion of $(x + 3)^3$ is
Question 2 :
Find the value of $k$, if $x-1$ is factor of $P(x)$ and $P(x)=3x^{2}+kx+\sqrt {2}$
Question 3 :
Given that $x = 2$ is a solution of $x^3 - 7x + 6 = 0$. The other solutions are
Question 4 :
If both $x + 1$ and $x-  1$ are factors of $ax^3 + x^2+  2a + b = 0$, find the values of $a$ and $b$ respectively.
Question 6 :
Using remainder theorem, find the reminder when $x^3-ax^2+2x-a$ is divided by $x-a$.
Question 7 :
If $x + a$ is a factor of $x^{4} - a^{2}x^{2} + 3x - 6a$, then $a =$
Question 9 :
The remainder obtained by dividing $x^{n} - \dfrac{a}{b}$ by $ax - b$ is<br/>
Question 10 :
Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder. <br/>$p(x)=x^3-3x^2+5x-3$<br/>$ g(x)=x^2-2$<br/>
Question 11 :
If n is an integer, what is the remainder when $5x^{2n + 1}- 10x^{2n} + 3x^{2n-1} + 5$ is divided by x + 1?
Question 12 :
Which of the following should be added to $\displaystyle 9x^{3}+6x^{2}+x+2$ so that the sum is divisible by $(3x + 1)$?
Question 13 :
The polynomials $p\left( x \right) = k{x^3} + 3{x^2} - 3$ and $Q\left( x \right) = 2{x^3} - 5x + k$, when divided by (x - 4) leave the same remainder. The value of K is
Question 14 :
If $ax^{3}+ bx^{2}+ c x + d$ is divided by $x - 2$, then the remainder is equal<br>
Question 15 :
Let p(x) be a quadratic polynomial such that $p(0)=1$. If p(x) leaves remainder $4$ when divided by $x-1$ and it leaves remainder $6$ when divided by $x+1$; then which one is correct?
