📚 Topic Summary
Subtracting polynomials vertically involves aligning like terms (terms with the same variable and exponent) in columns and then subtracting the coefficients. Remember to distribute the negative sign to each term in the polynomial being subtracted. This process simplifies complex polynomial subtraction into a more manageable format, minimizing errors.
🧠 Part A: Vocabulary
Match the following terms with their definitions:
- Polynomial
- Coefficient
- Like Terms
- Constant
- Variable
- A symbol (usually a letter) representing a value that can change.
- Terms that have the same variable(s) raised to the same power(s).
- A number multiplied by a variable in a term.
- An expression consisting of variables, coefficients, and constants, combined using addition, subtraction, and non-negative integer exponents.
- A fixed value that does not change.
📝 Part B: Fill in the Blanks
When subtracting polynomials vertically, it's important to align the ________ terms. This means putting terms with the same ________ and ________ in the same column. Remember to ________ the negative sign when subtracting. After aligning, you can subtract the ________ of the like terms. The result will be another ________.
🧪 Part C: Critical Thinking
Explain why it's important to distribute the negative sign when subtracting polynomials. What happens if you forget to do this?
➗ Worksheet: Subtracting Polynomials Vertically
Subtract the following polynomials vertically. Show your work!
- $(5x^2 + 3x - 2) - (2x^2 - x + 4)$
- $(7x^3 - 4x + 1) - (3x^3 + 2x^2 - 5)$
- $(4x^2 - 6x + 9) - (x^2 + 6x - 3)$
- $(-2x^3 + 5x - 7) - (4x^3 - 3x^2 + 2)$
- $(x^4 + 2x^2 - 8) - (3x^4 - x^2 + 1)$
- $(6x^3 - x + 5) - (-2x^3 + 4x^2 - 1)$
- $(-3x^2 + 7x - 4) - (5x^2 - 2x + 6)$