-(5x%5E3%2B12x%5E2-3x-4).jpeg "(3x^3-2x^2+4x-8)-(5x^3+12x^2-3x-4)")
Subtracting Polynomials: A Step-by-Step Guide
This article will guide you through the process of subtracting the polynomials (3x^3-2x^2+4x-8) and (5x^3+12x^2-3x-4).
Understanding the Basics
Before we start, it's crucial to understand some key concepts:
- Polynomials: An algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
- Like Terms: Terms that have the same variables raised to the same exponents.
- Subtracting Polynomials: Subtracting polynomials involves combining like terms after distributing the negative sign.
The Steps
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Rewrite the Problem: Begin by rewriting the problem with the second polynomial in parentheses, preceded by a negative sign.
(3x^3 - 2x^2 + 4x - 8) - (5x^3 + 12x^2 - 3x - 4)
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Distribute the Negative Sign: Distribute the negative sign to each term within the second set of parentheses.
3x^3 - 2x^2 + 4x - 8 - 5x^3 - 12x^2 + 3x + 4
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Combine Like Terms: Identify and combine the like terms, remembering that the coefficients are added or subtracted depending on their signs.
(3x^3 - 5x^3) + (-2x^2 - 12x^2) + (4x + 3x) + (-8 + 4)
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Simplify: Perform the arithmetic on the coefficients, preserving the variables and their exponents.
-2x^3 - 14x^2 + 7x - 4
The Result
Therefore, the result of subtracting the polynomials (3x^3-2x^2+4x-8) and (5x^3+12x^2-3x-4) is -2x^3 - 14x^2 + 7x - 4.
Key Points to Remember:
- Always distribute the negative sign carefully.
- Combine only like terms.
- Simplify the expression to its simplest form.
By following these steps, you can confidently subtract any two polynomials.