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Division of Polynomial by a Polynomial Video Lecture | Mathematics for Super TET
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FAQs on Division of Polynomial by a Polynomial Video Lecture - Mathematics for Super TET
| 1. What is polynomial division? |  |
Ans. Polynomial division is a process in algebra where one polynomial is divided by another polynomial to obtain a quotient and a remainder. It is similar to dividing numbers, but instead of numbers, we deal with polynomials.
| 2. How do you divide a polynomial by a polynomial? | |
Ans. To divide a polynomial by a polynomial, we use the long division method. We divide the polynomial in a similar way to how we divide numbers. We divide the highest degree term of the dividend by the highest degree term of the divisor, then multiply the divisor by the resulting quotient and subtract it from the dividend. This process is repeated until we obtain a remainder with a degree lower than the divisor.
| 3. What is the significance of polynomial division? | |
Ans. Polynomial division is significant because it helps us simplify and solve polynomial equations. By dividing a polynomial equation, we can determine if a given polynomial is a factor of another polynomial, or find the quotient and remainder when dividing two polynomials. This process allows us to manipulate and work with polynomials in various mathematical applications.
| 4. Can you divide a polynomial by a polynomial with higher degree? | |
Ans. No, it is not possible to divide a polynomial by a polynomial with a higher degree. In polynomial division, the degree of the divisor must be equal to or lower than the degree of the dividend. If the divisor has a higher degree, the division cannot be performed. However, if the divisor is a factor of the dividend, the division will result in a quotient of lower degree and a remainder of zero.
| 5. Are there any special cases in polynomial division? | |
Ans. Yes, there are special cases in polynomial division. One special case is when the divisor is a linear polynomial of the form (ax + b), where a and b are constants. In this case, we can use the factor theorem to determine if the divisor is a factor of the dividend. If the remainder of the division is zero, then the divisor is a factor. Another special case is when the divisor is a quadratic polynomial, and we can use synthetic division to perform the division quickly.
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