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Explanation: On multiplying the unit digit of N we get, 1*3*5=15. 15 when divided by 12 gives 3 as remainder. Therefore, remainder when N=1521*1523*1525 is divisible by 12 is 3.
Remainder Theorem - Dealing with large powers. If you can express the expression in the form (ax+1)n a the remainder will become 1 directly. In such a case, no matter how large the value of the power n is, the remainder is 1. Example : (3712654) 9 = (9∗4+1)12654 9 = 1.
REMAINDER THEOREM PRACTICE QUESTIONS. (1) Check whether p (x) is a multiple of g (x) or not . p (x) = x 3 - 5x 2 + 4x - 3 ; g (x) = x – 2. Solution. (2) By remainder theorem, find the remainder when, p (x) is divided by g (x) where, (i) p (x) = x 3 - 2x 2 - 4x - 1 and g (x) = x + 1.
The remainder theorem says "when a polynomial p (x) is divided by a linear polynomial whose zero is x = k, the remainder is given by p (k)". The basic formula to check the division is: Dividend = (Divisor × Quotient) + Remainder. The remainder theorem does not work when the divisor is not linear.
What is the Remainder Theorem? Examples. Proof of the Remainder Theorem. A Special Case – The Factor Theorem. In this tutorial, we will learn about the polynomial remainder theorem. But before we can do that, there are a couple of things we need to address first. Polynomials and Their Notation.
The Polynomial Remainder Theorem simplifies the process of finding the remainder when dividing a polynomial by \[x - a\]. Instead of long division, you just evaluate the polynomial at \[a\]. This method saves time and space, making polynomial division more manageable.
The Polynomial Remainder Theorem allows us to determine whether a linear expression is a factor of a polynomial expression easily. It tells us the remainder when a polynomial is divided by \[x - a\] is \[f(a)\]. This means if \[x - a\] is a factor of the polynomial, the remainder is zero.
