1. Let's clarify the problem: You want to understand how to subtract polynomials. 2. Subtracting polynomials means taking one polynomial and subtracting another from it. 3. For example, if you have two polynomials $P(x) = 3x^2 + 5x - 2$ and $Q(x) = x^2 - 4x + 1$, subtracting $Q(x)$ from $P(x)$ means computing $P(x) - Q(x)$. 4. Write the subtraction explicitly: $$P(x) - Q(x) = (3x^2 + 5x - 2) - (x^2 - 4x + 1)$$ 5. Remove the parentheses carefully, remembering to distribute the minus sign to each term in $Q(x)$: $$= 3x^2 + 5x - 2 - x^2 + 4x - 1$$ 6. Combine like terms: - Combine $3x^2$ and $-x^2$ to get $2x^2$ - Combine $5x$ and $4x$ to get $9x$ - Combine $-2$ and $-1$ to get $-3$ 7. The result is: $$2x^2 + 9x - 3$$ 8. So, subtracting polynomials involves changing the signs of the second polynomial's terms and then combining like terms. This method works for any polynomials you want to subtract.