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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.
The remainder theorem in Class 9 is used to find the remainder when a polynomial p(x) is divided by (ax + b). The remainder theorem is further extended to prove the factor theorem where we can determine whether (ax + b) is a factor of p(x) or not.
Polynomial of Class 9. REMAINDER THEOREM. Let p (x) be any polynomial of degree greater than or equal to 1 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 one.
Sep 10, 2024 · The Remainder Theorem states that when a polynomial f (x) is divided by a linear polynomial of the form (x – a), the remainder is simply the value of the function evaluated at x = a. This simplifies polynomial division, allowing us to bypass long division in certain cases.
We shall also study the Remainder Theorem and Factor Theorem and their use in the factorisation of polynomials. In addition to the above, we shall study some more algebraic identities and their use in factorisation and in evaluating some given expressions. 2.2 Polynomials in One Variable.
What is the Remainder theorem? Suppose p (x) is a polynomial of degree at least 1 and a is any real number. When p (x) is divided by (x − a), the remainder will be p (a). Thus, the Remainder theorem for polynomials can be written as: p (x) = (x – a) q (x) + r. Here, p (x) = Dividend. (x – a) = Divisor. q (x) = Quotient. r = 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.
Apr 16, 2024 · Chapter 2 Class 9 Polynomials. Concept wise. Remainder Theoram. Remainder Theorem. Last updated at April 16, 2024 by Teachoo. Let us find remainder when p (x) is divided by g (x) p (x) = x 3 − 3x 2 + 4x + 10. g (x) = x + 1. By Long Division. So, Remainder = 2. There is another method to find remainder by Remainder Theorem. Remainder Theorem.
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 ). Example: 2a2 - 5a - 1 is divided by a – 3. Solution: Here p (a) = 2a2 - 5a - 1.
The NCERT Solutions Class 9 Maths Chapter 2 includes a detailed explanation of the remainder and the factor theorem, which hold an important place in algebra. Also, the crucial algebraic identities are discussed in an elaborate manner with plenty of questions to solve for the students.
