Class 9 > Crash Course: Class 9 > Video: Remainder Theorem of Polynomials (Old Syllabus)
Video: Remainder Theorem of Polynomials (Old Syllabus) Video Lecture - Crash Course: Class 9
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FAQs on Video: Remainder Theorem of Polynomials (Old Syllabus) Video Lecture - Crash Course: Class 9
| 1. What is the Remainder Theorem of Polynomials? |  |
The Remainder Theorem of Polynomials states that if a polynomial function P(x) is divided by (x - a), then the remainder of the division is equal to P(a). In simpler terms, when we divide a polynomial by (x - a), the remainder we get is the value of the polynomial when we substitute x = a.
| 2. How do you use the Remainder Theorem to find the remainder of a polynomial division? | |
To use the Remainder Theorem to find the remainder of a polynomial division, substitute the value of the divisor (x - a) into the polynomial function. Evaluate this expression to find the remainder.
| 3. Can the Remainder Theorem be used to find the quotient of a polynomial division? | |
No, the Remainder Theorem only allows us to find the remainder of a polynomial division. To find the quotient, we need to perform the long division or synthetic division process.
| 4. How can the Remainder Theorem be applied in real-life situations? | |
The Remainder Theorem can be applied in various real-life situations. One example is in finance, where it can be used to calculate the remaining balance of a loan or investment. In physics, it can help determine the remainder energy of a system after certain processes. The theorem also finds applications in engineering, computer science, and other fields.
| 5. Are there any limitations to the Remainder Theorem? | |
Yes, there are some limitations to the Remainder Theorem. It can only be applied when dividing by a linear factor of the form (x - a). Additionally, the theorem assumes that the divisor is not equal to zero, and the polynomial function is defined for all real numbers.
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