Subtract two polynomials.

Check the final answer first, then review the worked steps.

Problem

Subtract two polynomials.

Answer

\(-x^2 + 4x - 2\)

Step-by-step solution

1. Identify the polynomials: The problem asks to subtract the polynomial $10x^2 + 3$ from the polynomial $9x^2 + 4x + 1$.
2. Set up the subtraction: To subtract one polynomial from another, we write the second polynomial minus the first polynomial. This is written as: $$(9x^2 + 4x + 1) - (10x^2 + 3)$$
3. Distribute the negative sign: When subtracting a polynomial, we distribute the negative sign to each term inside the parentheses of the polynomial being subtracted. This changes the sign of each term: $$9x^2 + 4x + 1 - 10x^2 - 3$$
4. Group like terms: Combine terms that have the same variable and exponent. In this case, we group the $x^2$ terms and the constant terms: $$(9x^2 - 10x^2) + 4x + (1 - 3)$$
5. Combine like terms: Perform the addition or subtraction for each group of like terms: $$-x^2 + 4x - 2$$

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