-(x%5E4%2B5x%5E3%2B8x%5E2%2Bx%2B5).jpeg "(5x^4-4x^3-2x^2+x-19)-(x^4+5x^3+8x^2+x+5)")
Subtracting Polynomials: A Step-by-Step Guide
This article will guide you through the process of subtracting the polynomials (5x^4-4x^3-2x^2+x-19) and (x^4+5x^3+8x^2+x+5).
Understanding the Process
Subtracting polynomials involves combining like terms. This means identifying terms with the same variable and exponent and then performing the subtraction operation on their coefficients.
Step 1: Distribute the Negative Sign
The subtraction sign in front of the second polynomial acts like a negative one, affecting each term inside the parentheses. This means we distribute the negative sign:
(5x^4-4x^3-2x^2+x-19) - (x^4+5x^3+8x^2+x+5)
becomes:
(5x^4-4x^3-2x^2+x-19) + (-x^4-5x^3-8x^2-x-5)
Step 2: Combine Like Terms
Now that the negative sign is distributed, we can combine like terms:
- x^4 terms: 5x^4 - x^4 = 4x^4
- x^3 terms: -4x^3 - 5x^3 = -9x^3
- x^2 terms: -2x^2 - 8x^2 = -10x^2
- x terms: x - x = 0
- Constant terms: -19 - 5 = -24
Step 3: Write the Result
Combining all the simplified terms, we get the final answer:
4x^4 - 9x^3 - 10x^2 - 24
Conclusion
Subtracting polynomials is a straightforward process that involves distributing the negative sign and combining like terms. By following these steps, you can effectively subtract polynomials and arrive at the correct answer.