๐ Topic Summary
Subtracting polynomials vertically is a method of polynomial subtraction that organizes the terms in columns based on their degree. This makes it easier to combine like terms. Remember to distribute the negative sign to each term of the polynomial being subtracted before combining. This will help you avoid common mistakes and ensure you get the correct answer.
For example, to subtract $(3x^2 + 2x - 1)$ from $(5x^2 - x + 4)$, you would write them vertically, aligning like terms. Then, distribute the negative sign to the second polynomial, changing it to $(-3x^2 - 2x + 1)$. Finally, combine the terms in each column:
$ \begin{array}{r} 5x^2 - x + 4 \\ - (3x^2 + 2x - 1) \\ \hline \\ 5x^2 - x + 4 \\ -3x^2 - 2x + 1 \\ \hline 2x^2 - 3x + 5 \end{array} $
๐งฎ Part A: Vocabulary
Match the term with the correct definition:
- Polynomial
- Term
- Coefficient
- Constant
- Like Terms
- A value that does not change.
- Terms that have the same variable raised to the same power.
- A mathematical expression consisting of variables and coefficients, combined using addition, subtraction, multiplication, and non-negative integer exponents.
- A number multiplied by a variable in a term.
- A single number or variable, or numbers and variables multiplied together.
๐ Part B: Fill in the Blanks
When subtracting polynomials vertically, it's important to align the ______ terms. Remember to ______ the negative sign to each term of the polynomial being subtracted. This means changing the ______ of each term. After distributing the negative sign, ______ like terms to simplify the expression.
๐ค Part C: Critical Thinking
Explain why distributing the negative sign is important when subtracting polynomials. What happens if you forget to distribute the negative sign?