%2B(-p%5E3-8p%5E2-15p)-find-the-sum.jpeg "(-3p^3+5p^2-2p)+(-p^3-8p^2-15p) Find The Sum")
Finding the Sum of Polynomials
This article will guide you through the process of finding the sum of two polynomials: (-3p^3+5p^2-2p) + (-p^3-8p^2-15p).
Understanding Polynomials
Polynomials are expressions that consist 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.
Combining Like Terms
To find the sum of two polynomials, we combine their like terms. Like terms are those with the same variable(s) raised to the same power.
Let's break down the given problem step-by-step:
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Identify Like Terms:
- p^3 terms: -3p^3 and -p^3
- p^2 terms: 5p^2 and -8p^2
- p terms: -2p and -15p
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Combine Coefficients:
- p^3 terms: -3p^3 + (-p^3) = -4p^3
- p^2 terms: 5p^2 + (-8p^2) = -3p^2
- p terms: -2p + (-15p) = -17p
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Combine the Results:
- Final Sum: -4p^3 - 3p^2 - 17p
Conclusion
Therefore, the sum of the polynomials (-3p^3+5p^2-2p) and (-p^3-8p^2-15p) is -4p^3 - 3p^2 - 17p.