A).What is the real root of the equation

b). Solve for x and write answers in interval notation

c). rewrite the expression as a a power of x.
d). Simplify the fractional expression
e). The sum of the first n terms of a series is given by : Sn= 2n(n+3). Show that the terms of the series form an arithmetic progression...

f). A species of extremely rare, deep water fish has an extremely long life span and rarely have children. If there are a total of 821 of this type of fish and their growth rate is 2% each month, how many will there be in half a year? What will the population be in 10years and in 100years [Hint: write a mathematical equation using: P-population, Po- initial population, r- rate, t- time]

g). Prove: if a, b,c and d are positive numbers such that a<b and c<d, than ac<bd

h). You are to define a new mathematical operation using the symbol (.) This operation is defined as; a. b= 2. a + b= 2a + b
Give an example to show that the above operation is neither commutative nor associative.

I). Show that
J). Factorise the expression
k). Two cubic polynomials are defined by
where a and b are constants
i). given f(x) and g(x) have two common factors
show that a = - 4 and find the value of b

ii). use the values of a and b to factorise f(x) fully. Hence show that f(x) and g(x) have 2 common factors

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