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Factorise the polynomial.? - Class 10 PDF Download
🤔😏FAQs on Factorise the polynomial.? - Class 10
| 1. How do you factorise a polynomial? |  |
Ans. To factorise a polynomial, you need to find its factors or expressions that can be multiplied together to obtain the original polynomial. This can be done by using various methods such as grouping, factoring out common factors, or using algebraic identities.
| 2. What is the importance of factorising a polynomial? | |
Ans. Factoring a polynomial is important as it helps us understand its properties and behavior. It allows us to find the roots or zeros of the polynomial, which are the values that make the polynomial equal to zero. Additionally, factorising can simplify complex polynomial expressions and make them easier to work with in calculations.
| 3. Can all polynomials be factorised? | |
Ans. Not all polynomials can be factorised. Some polynomials, known as irreducible or prime polynomials, cannot be expressed as a product of simpler polynomials. For example, the polynomial x^2 + 1 is irreducible over the real numbers and cannot be factorised further.
| 4. What are the different methods of factorising a polynomial? | |
Ans. There are several methods to factorise a polynomial, including:
1. Factoring out the greatest common factor (GCF): Identify the highest common factor of all the terms and divide it out.
2. Grouping: Group the terms in pairs and then factor out the common factors from each pair.
3. Difference of squares: If the polynomial is in the form a^2 - b^2, it can be factorised as (a + b)(a - b).
4. Perfect square trinomial: If the polynomial is in the form a^2 + 2ab + b^2 or a^2 - 2ab + b^2, it can be factorised as (a + b)^2 or (a - b)^2.
5. Quadratic trinomial: If the polynomial is a quadratic trinomial, it can be factorised using the quadratic formula or by factoring the product of two binomials.
| 5. Can a polynomial have more than one way to be factorised? | |
Ans. Yes, a polynomial can have multiple ways to be factorised. This is because there are different methods and techniques that can be applied to factorise polynomials. Additionally, the order in which the factors are written can vary, but the product of the factors will remain the same.
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Nov 09, 2024 Last updated |
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