As a result; there is still only a single pair of rabbits.
After duration of two months, the initial pair of rabbits will give birth to another pair. There will be two pairs.
After duration of three months, the initial pair will give birth again, the second pair mate, but do not give birth. This makes three pair.
When four months will elapse, the original pair gives birth, and the pair born in the second month gives birth. The pair that is born in month in the third month will mate, but will not give birth. This will make two new pairs, thereby making a total of five pair.
After duration of five months, each pair that was alive two months earlier will give birth. This will make three new pair, totaling to eight (Anderson, Frazier, and Popendorf, 1999)
Factor Theorem:
Value a is a root of polynomial p (x) when and only when (***) is a factor of p (x).
Evidence
1. (=)) Assuming that a is one of the roots of polynomial p (x). This implies that p (a) = 0.
Using the remainder theorem, we can conclude that remainder after being divided by (***) has to be zero. Therefore,
P (x) = (***) ¢ q (x) + 0
P (x) = (***) ¢ q (x)
Hence, (***) is a factor of p (x).
To establish the factors of a polynomial one can speedily substitute in values of x to find out which will provide you with a value of zero.
Example 1: Given f (x) = x3 + x2 -- 4x -- 4. Use the factor theorem to find a factor f (x) = x3 + x2 -- 4x -- 4
f (1) = (1)3 + (1)2 -- ( ) -- 4
(x -- 1) is not a factor f (2) = (2)3 + (2)2 -- ( ) -- 4
= 0 ?(x -- 2) is a factor
To move away from the value x to the factor merely place it into a bracket and then change the sign.
Rational Root (zero) Theorem
The Rational Zero Theorem provides a list of probable rational zeros of the polynomial function. The theorem provides all potential rational roots of the polynomial equation. Not all numbers in the list shall be a zero belonging to the function, however all rational zeros belonging to the polynomial function shall come out somewhere in the list.
The rational root theorem is also a test that is capable of being used to get the probable number of rational solutions or sometimes roots of the polynomial equation having coefficients which are integers.
Degree
The degree of a monomial equals to the sum of the exponents of individual variables that appears in the monomial. For example, the degree of x2yz3 is 2 + 1 + 3(Beckmann, 1976)
A polynomial is a monomial. It can also be said to be the algebraic sum or sometimes the difference of monomials. A polynomial degree is the greatest of the degrees of its terms after the combination of like terms. The leading coefficient is described as the coefficient of the term with the greatest. The polynomials which are having one, two or even three terms are referred to as monomials, binomials and trinomials in that order (Buchanan, 2010)
The degree of a monomial can simply be defined as the exponent or power that the monomial is raised to. If there exists three or more monomials that are being added or subtracted so as to make a polynomial, and each of them has a degree and the monomial having the highest degree are representing the whole degree of the polynomial.
The fundamental theory of algebra
It is one of the most essential results in mathematics.
The Fundamental Theorem of Algebra is practically basic spontaneously. It states that provided...
Aristoxenos, two centuries after Pythagoras released his model, sought to discredit the standing theories held by Pythagorean devotees. In his works, he established that numbers are not relevant to music, and that music is based on perception of what one hears, not any mathematical equation. Descartes as well as Vincenzo Galilei (Galileo's father) both also discredited the music-to-math theories that formed the revolutionary basis for Pythagoras' music work, but not
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