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Factor Theorem : Polynomials - Mathematics, Class 9 Video Lecture
FAQs on Factor Theorem : Polynomials - Mathematics, Class 9 Video Lecture
| 1. What is the factor theorem in polynomials? |  |
Ans. The factor theorem states that if a polynomial f(x) has a factor (x - a), then f(a) = 0. In other words, if substituting the value 'a' into the polynomial results in a zero, then (x - a) is a factor of the polynomial.
| 2. How can we use the factor theorem to factorize polynomials? | |
Ans. To factorize a polynomial using the factor theorem, we can follow these steps:
1. Identify a possible factor by setting f(a) = 0, where 'a' is a potential root of the polynomial.
2. Use long division or synthetic division to divide the polynomial by (x - a).
3. Repeat the process with the resulting quotient until we obtain a completely factored form of the polynomial.
| 3. Can the factor theorem be used to find all the factors of a polynomial? | |
Ans. No, the factor theorem can only help us find the linear factors of a polynomial. If a polynomial has a factor of degree higher than 1, the factor theorem alone cannot determine it. In such cases, we may need to use other methods like polynomial long division or synthetic division to find the remaining factors.
| 4. How is the factor theorem related to the remainder theorem? | |
Ans. The factor theorem and the remainder theorem are closely related. The factor theorem states that if (x - a) is a factor of a polynomial f(x), then f(a) = 0. On the other hand, the remainder theorem states that if we divide a polynomial f(x) by (x - a), the remainder will be f(a). In essence, the factor theorem is a specific case of the remainder theorem where the remainder is zero.
| 5. Can the factor theorem be applied to all types of polynomials? | |
Ans. The factor theorem is applicable to all types of polynomials, including both monic and non-monic polynomials. It can be used to find the factors of polynomials with real coefficients, complex coefficients, or even polynomials with irrational coefficients. However, it is important to note that the factor theorem only applies to linear factors (x - a) and cannot be used to find factors of higher degree.
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Oct 12, 2025
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