📚 Topic Summary
Adding polynomials horizontally involves identifying and combining like terms. Like terms are terms that have the same variable raised to the same power. When adding, simply add the coefficients (the numbers in front of the variables) of the like terms and keep the variable and exponent the same. For example, to add $(3x^2 + 2x + 1)$ and $(x^2 - x + 4)$, you combine $3x^2$ and $x^2$ to get $4x^2$, $2x$ and $-x$ to get $x$, and $1$ and $4$ to get $5$. The final answer is $4x^2 + x + 5$.
Remember, you can only combine terms that are 'like'. Trying to combine $x^2$ and $x$ is like trying to add apples and oranges – they are different!
🧠 Part A: Vocabulary
Match the following terms with their definitions:
- Term
- Coefficient
- Variable
- Polynomial
- Like Terms
- 🔢 A symbol (usually a letter) that represents a value.
- ➕ A number that multiplies a variable.
- 🧮 Parts of an expression separated by + or - signs.
- ➕ An expression with one or more terms.
- 🧲 Terms that have the same variable raised to the same power.
(Match the numbered terms to the lettered definitions. e.g., 1-A, 2-B, etc.)
✍️ Part B: Fill in the Blanks
When adding polynomials horizontally, it's important to identify the _______ _______. These are terms with the same _______ raised to the same _______. You then add the _______ of these like terms, keeping the variable and exponent the same. For example, in the expression $2x^2 + 3x + 5x^2$, $2x^2$ and $5x^2$ are _______ _______, and their sum is _______.
🤔 Part C: Critical Thinking
Explain in your own words why it is important to only combine 'like terms' when adding polynomials. What happens if you try to combine unlike terms?