What does remainder theorem mean?

The Remainder Theorem Definition states that when a polynomial is p ( a ) is divided by another binomial ( a – x ), then the remainder of the end result that is obtained is p ( x ).

What is remainder theorem in Class 9?

The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial \[\left( x-a \right)\] then the remainder of that division will be equal to f(a). 7 divided by 2 equals 3 with remainder 1, where 7 is dividend, 2 is divisor, 3 is quotient and 1 is remainder.

What is remainder theorem Class 10?

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.

What is factor theorem Class 10?

According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0. Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0.

What is remainder theorem definition Class 9?

Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a). Proof: Let p(x) be any polynomial with degree greater than or equal to 1.

How do you calculate a remainder?

How to calculate the remainder Begin with writing down your problem. Decide on which of the numbers is the dividend, and which is the divisor. Perform the division – you can use any calculator you want. Round this number down. Multiply the number you obtained in the previous step by the divisor.

How do you find the remainder of a polynomial?

The Remainder Theorem. Then the Theorem talks about dividing that polynomial by some linear factor x – a, where a is just some number. Then, as a result of the long polynomial division, you end up with some polynomial answer q ( x) (the ” q ” standing for “the quotient polynomial”) and some polynomial remainder r ( x).

What is the definition for a remainder in math?

In mathematics, the remainder is the amount “left over” after performing some computation. In arithmetic , the remainder is the integer “left over” after dividing one integer by another to produce an integer quotient ( integer division ).

What is the residue theorem?

Residue theorem. In complex analysis, the residue theorem, sometimes called Cauchy ‘s residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well.