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Video: Factor Theorem Video Lecture - Class 9

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FAQs on Video: Factor Theorem Video Lecture - Class 9

1. What is the Factor Theorem and how is it used in algebra?
Ans. The Factor Theorem is a fundamental concept in algebra that helps in finding factors of polynomial expressions. It states that if a polynomial f(x) has a factor (x - a), then the value a is a root of the polynomial. By using the Factor Theorem, we can factorize polynomials and find their roots.
2. How can the Factor Theorem be applied to solve polynomial equations?
Ans. To solve polynomial equations using the Factor Theorem, we first need to factorize the polynomial expression. By factoring the polynomial, we can identify the factors and their corresponding roots. We set each factor equal to zero and solve for the roots, which gives the values of x that make the polynomial equal to zero. These values are the solutions to the polynomial equation.
3. Can the Factor Theorem be used to find the roots of any polynomial?
Ans. Yes, the Factor Theorem can be used to find the roots of any polynomial. If a polynomial has a factor (x - a), then the value a is a root of the polynomial. By applying the Factor Theorem and factoring the polynomial, we can identify all the roots or solutions of the polynomial equation.
4. Is the Factor Theorem only applicable to quadratic equations?
Ans. No, the Factor Theorem is not limited to quadratic equations. It can be used to find the roots of polynomials of any degree. The Factor Theorem is a general concept that applies to all polynomial expressions, regardless of their degree.
5. How does the Factor Theorem relate to the process of polynomial division?
Ans. The Factor Theorem is closely related to the process of polynomial division. If a polynomial f(x) has a factor (x - a), then dividing f(x) by (x - a) will yield a quotient polynomial. The remainder of the division will be zero if (x - a) is indeed a factor of f(x). This connection allows us to verify if a given expression is a factor of a polynomial using polynomial division.
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