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Remainder Theorem - Class 9 Video Lecture
FAQs on Remainder Theorem - Class 9 Video Lecture
| 1. What is the Remainder Theorem? |  |
Ans. The Remainder Theorem is a mathematical concept that states that when a polynomial f(x) is divided by (x-a), the remainder obtained will be equal to f(a). In other words, if we substitute the value of 'a' into the polynomial and evaluate it, the result will be the same as the remainder obtained when dividing the polynomial by (x-a).
| 2. How can the Remainder Theorem be used to find remainders? | |
Ans. To use the Remainder Theorem to find remainders, we need to divide the polynomial by the given factor (x-a), where 'a' is a constant. We then substitute the value of 'a' into the polynomial, and the result will be the remainder. By using this theorem, we can quickly calculate remainders without performing long division.
| 3. Can the Remainder Theorem be used to factorize polynomials? | |
Ans. Yes, the Remainder Theorem can be used to factorize polynomials. If we have a polynomial f(x) and we know that (x-a) is a factor of the polynomial, we can use the Remainder Theorem to find the value of 'a'. Once we find 'a', we can then use polynomial division to divide f(x) by (x-a) and obtain the other factor(s) of the polynomial.
| 4. What is the significance of the Remainder Theorem in solving equations? | |
Ans. The Remainder Theorem is significant in solving equations as it helps us determine whether a given value is a solution or not. If we substitute a value 'a' into a polynomial equation and the remainder is zero, then 'a' is a solution to the equation. This allows us to solve polynomial equations efficiently by checking for values that satisfy the Remainder Theorem.
| 5. Are there any limitations to the application of the Remainder Theorem? | |
Ans. Yes, there are limitations to the application of the Remainder Theorem. This theorem can only be used for polynomial functions and does not apply to other types of functions. Additionally, the Remainder Theorem only helps us find remainders when dividing by linear factors (x-a). It cannot be used to find remainders when dividing by quadratic or higher degree factors.
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Nov 25, 2024 Last updated |
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