University Maths Solution
Maths Question  

Question 1 
If the two roots of the equation ${{x}^{4}}+a{{x}^{3}}+b{{x}^{2}}+cx+d=0$ are such that one is the negative of the other, show that ${{c}^{2}}=a(bcad)$

Question 2 
$\text{Show that the polynomial }{{x}^{4}}+4{{x}^{3}}+6{{x}^{2}}8\text{ is divisible by }x+2$ 
Question 3 
$\text{By using the remainder theorem, factorise completely }{{x}^{4}}10{{x}^{3}}+35{{x}^{2}}50x+24$ 
Question 4 
$\begin{align} & \text{Given that }x1\text{ and }x2\text{ are factors of the polynomial }{{x}^{3}}+a{{x}^{2}}+bx6.\text{ } \\ & \text{Find }a\text{ and }b \\\end{align}$ 
Question 5 
$\text{Find the remainder when }{{x}^{4}}3{{x}^{3}}+4{{x}^{2}}6x+7\text{ is divided by }x1$ 
Question 6 
$\begin{align} & \text{Use the remainder theorem to factorise completely the expression}\, \\ & {{x}^{3}}(yz)+{{y}^{3}}(zx)+{{z}^{3}}(xy) \\\end{align}$ 
Question 7 
$\text{Solve the equation by using Remainder theorem }{{x}^{4}}16{{x}^{3}}+80{{x}^{2}}176x+105=0$ 
Question 8 
$\begin{align} & \text{Solve the following equation by using Remainder theorem} \\ & \text{ }{{x}^{3}}15{{x}^{2}}+74x120=0 \\\end{align}$ 
Question 9 
$\begin{align} & \text{Solve the following equation by using Remainder theorem} \\ & {{x}^{3}}(5+a){{x}^{2}}+(6+5a)x6a=0 \\\end{align}$ 