%2B(11x%5E4-4x%5E2-11x-9).jpeg "(9x^4-3x^3+4x^2+5x+7)+(11x^4-4x^2-11x-9)")
Adding Polynomials: A Step-by-Step Guide
This article will guide you through the process of adding two polynomials: (9x⁴ - 3x³ + 4x² + 5x + 7) + (11x⁴ - 4x² - 11x - 9)
Understanding Polynomials
Polynomials are algebraic expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term in a polynomial is a product of a coefficient and one or more variables raised to non-negative integer powers.
Adding Polynomials
To add polynomials, we combine like terms. Like terms are terms that have the same variables raised to the same powers.
Here's how to add the given polynomials:
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Arrange the terms in descending order of their exponents: (9x⁴ - 3x³ + 4x² + 5x + 7) + (11x⁴ - 4x² - 11x - 9)
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Identify like terms:
- x⁴ terms: 9x⁴ + 11x⁴
- x³ terms: -3x³
- x² terms: 4x² - 4x²
- x terms: 5x - 11x
- Constant terms: 7 - 9
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Combine like terms by adding their coefficients:
- (9 + 11)x⁴ - 3x³ + (4 - 4)x² + (5 - 11)x + (7 - 9)
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Simplify the expression:
- 20x⁴ - 3x³ - 6x - 2
Final Result
Therefore, the sum of the given polynomials is 20x⁴ - 3x³ - 6x - 2.
Key Points
- Remember to add only like terms.
- Always combine the coefficients of the like terms.
- Organize the terms in descending order of their exponents.
- Simplify the expression by combining constants.