REMAINDER THEOREM Meaning and
Definition
-
The remainder theorem is a fundamental concept in algebra and polynomial division. It states that if a polynomial function P(x) is divided by a linear divisor (x-a), the remainder obtained will be the value of P(a). In other words, when P(x) is divided by (x-a), the remainder is equal to P(a).
To understand this theorem, it is essential to grasp the concept of polynomial division. Polynomial division is an arithmetic process used to divide two polynomials in order to find the quotient and remainder. The remainder theorem provides a shortcut to calculate the remainder when dividing a polynomial by a linear factor.
The theorem is derived from the polynomial division algorithm, where P(x) is divided by (x-a). When performing polynomial division, one can write P(x) as the product of (x-a) and the quotient Q(x), plus the remainder R. By substituting x=a into the polynomial equation, P(a) is obtained. This result represents the remainder when P(x) is divided by (x-a).
The remainder theorem is widely used in various applications of algebra, including solving equations, factoring polynomials, and analyzing graphs. It allows mathematicians to determine whether a given value is a root of a polynomial function and provides a method to find the maximum or minimum value of a polynomial by evaluating the remainder at specific points. The remainder theorem is a powerful tool that simplifies calculations and aids in understanding the properties of polynomials.
Common Misspellings for REMAINDER THEOREM
- eemainder theorem
- demainder theorem
- femainder theorem
- temainder theorem
- 5emainder theorem
- 4emainder theorem
- rwmainder theorem
- rsmainder theorem
- rdmainder theorem
- rrmainder theorem
- r4mainder theorem
- r3mainder theorem
- renainder theorem
- rekainder theorem
- rejainder theorem
- remzinder theorem
- remsinder theorem
- remwinder theorem
- remqinder theorem
- remaunder theorem
Etymology of REMAINDER THEOREM
The term "remainder theorem" is derived from the combination of the words "remainder" and "theorem".
1. Remainder: word "remainder" comes from the Middle English "remaindre", which originated from the Old French "remaindre". In turn, the Old French word is derived from the Latin "remanēre", which means "to remain" or "to be left behind". term "remainder" refers to what is left over after division or subtraction.
2.orem: term "theorem" comes from the Ancient Greek word "theōrēma", which means "a proposition to be proved" or "contemplation". In mathematical context, a theorem refers to a statement or proposition that has been proven through rigorous reasoning or logical deduction.
Thus, when combined together, "remainder theorem" refers to a specific mathematical proposition or rule that relates to the remainders obtained when dividing polynomials.
Infographic
Add the infographic to your website:
