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Mind Map: Polynomials | Mathematics (Maths) Class 9 PDF Download
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FAQs on Mind Map: Polynomials - Mathematics (Maths) Class 9
| 1. What are polynomials and how are they classified ? |  |
Ans. Polynomials are algebraic expressions that consist of variables raised to non-negative integer powers and coefficients. They can be classified based on the number of terms:
1. Monomial: An expression with one term (e.g., 3x²).
2. Binomial: An expression with two terms (e.g., 2x² + 3x).
3. Trinomial: An expression with three terms (e.g., x² + 2x + 1).
Additionally, they can be classified by their degree, which is the highest power of the variable (e.g., a polynomial of degree 3 has the form ax³ + bx² + cx + d).
| 2. How do you add and subtract polynomials ? | |
Ans. To add or subtract polynomials, you combine like terms. Like terms are those that have the same variable raised to the same power. For example, to add (3x² + 4x) and (2x² + 5), you combine the coefficients of like terms:
(3x² + 2x²) + 4x + 5 = 5x² + 4x + 5.
For subtraction, you subtract the coefficients of like terms:
(3x² + 4x) - (2x² + 5) = (3x² - 2x²) + 4x - 5 = x² + 4x - 5.
| 3. What is the significance of the degree of a polynomial ? | |
Ans. The degree of a polynomial is significant because it determines the polynomial's behavior and characteristics. The degree indicates the maximum number of roots (solutions) the polynomial can have. For instance, a polynomial of degree n can have up to n real roots. Additionally, the degree influences the graph of the polynomial, such as the number of turns it may have and its end behavior. Higher degree polynomials can exhibit more complex shapes compared to lower degree ones.
| 4. How can polynomials be factored ? | |
Ans. Polynomials can be factored by finding their roots or using various factoring techniques. Common methods include:
1. Factoring out the greatest common factor (GCF).
2. Factoring by grouping, where terms are grouped to find common factors.
3. Using special identities, such as difference of squares (a² - b² = (a + b)(a - b)) and perfect square trinomials.
4. Applying the quadratic formula for polynomials of degree 2 to find roots, then expressing the polynomial as a product of its linear factors.
| 5. What are some real-life applications of polynomials ? | |
Ans. Polynomials have various real-life applications, including:
1. Physics: Modeling motion and forces, where equations can be represented as polynomials.
2. Engineering: Designing structures and systems, as many design equations are polynomial functions.
3. Economics: Calculating profit and loss scenarios using polynomial equations to predict outcomes based on different variables.
4. Computer science: Algorithms for data processing often use polynomial time complexity for efficiency.
5. Biology: Modeling population growth and decay, where polynomial equations can represent growth rates.
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