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Video: Division Algorithm For Polynomials Video Lecture - Class 10

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FAQs on Video: Division Algorithm For Polynomials Video Lecture - Class 10

1. What is the division algorithm for polynomials?
Ans. The division algorithm for polynomials states that for any two polynomials, dividend and divisor, there exists a unique quotient and remainder such that when the dividend is divided by the divisor, the remainder is either zero or has a degree lower than the divisor.
2. How is the division algorithm applied to polynomials?
Ans. To apply the division algorithm to polynomials, we divide the dividend by the divisor using long division or synthetic division method. The resulting quotient and remainder satisfy the properties mentioned in the algorithm.
3. Can you explain the steps involved in the division algorithm for polynomials?
Ans. Sure! The steps involved in the division algorithm for polynomials are as follows: 1. Divide the first term of the dividend by the first term of the divisor to obtain the first term of the quotient. 2. Multiply the entire divisor by the first term of the quotient. 3. Subtract the obtained product from the dividend. 4. Repeat steps 1-3 with the new dividend (obtained in step 3) until the degree of the new dividend is lower than the divisor. 5. The final quotient obtained after all the divisions is the quotient of the polynomial division. 6. The remaining polynomial, if any, after division is the remainder.
4. Is the remainder always zero in polynomial division?
Ans. No, the remainder is not always zero in polynomial division. According to the division algorithm for polynomials, the remainder can be either zero or have a degree lower than the divisor. If the remainder is zero, it means that the divisor is a factor of the dividend. If the remainder is non-zero, it indicates that there is no exact division and there is a leftover polynomial.
5. Can the division algorithm for polynomials be used to factorize polynomials?
Ans. Yes, the division algorithm for polynomials can be used to factorize polynomials. By dividing a polynomial by its factors, we can determine the quotient and remainder. If the remainder is zero, it implies that the divisor is a factor of the polynomial. Therefore, the division algorithm helps in identifying the factors of a polynomial and can aid in the process of factorization.
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