Remainder Theorem:-
When f(x) is divided by (x-a) the remainder is f(a)
Tor example:-
f(x) x3-2x2+5x+8 divided by x-2
f(2) 8-8+10+8 = 18
So the remainder is 18 if there is no remainder then the divisor is a factor of the dividend.
Germain's Theorem is about Vibrating Elastic Plates.
"thales" has given this bpt theorem.
A postulate is assumed to be true while a theorem is proven to be true. The truth of a theorem will be based on postulates.
In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integergreater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors.
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
You cannot solve a theorem: you can prove the theorem or you can solve a question based on the remainder theorem.
Any rational number can be used in the remainder theorem: 4 does not have a special role.
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In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
The Remainder Theorem states that for a polynomial ( f(x) ), if you divide it by a linear factor of the form ( x - c ), the remainder of this division is equal to ( f(c) ). This means that by evaluating the polynomial at ( c ), you can quickly determine the remainder without performing long division. This theorem is useful for factoring polynomials and analyzing their roots.
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.The factor theorem states that a polynomial has a factor if and only if
F(a)
The number 4 is often used in solving problems with the Remainder Theorem because it represents a specific case where we evaluate polynomials at a given point. The Remainder Theorem states that when a polynomial ( f(x) ) is divided by ( x - c ), the remainder is ( f(c) ). By substituting ( c ) with 4, we can find the remainder of the polynomial when divided by ( x - 4 ). This is particularly useful in problems that require evaluating the polynomial at that specific point to determine the remainder.
The Remainder Theorem states that if you divide a polynomial ( f(x) ) by a linear divisor of the form ( x - c ), the remainder is simply ( f(c) ). To find the remainder, substitute the value ( c ) into the polynomial ( f(x) ) and calculate the result. The output will be the remainder of the division. This method significantly simplifies finding remainders without performing long division.