## 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.