Add Polynomials: Group Like Terms
Align terms with same variables and powers. Combine coefficients. Watch the mess disappear.
Equation
y = (3*x^2 + 2*x - 5) + (x^2 - 3*x + 7) - (1*x^2 - x + 2)
Graph
Table
| x | y |
|---|---|
| -3 | 27 |
| -2 | 12 |
| -1 | 3 |
| 0 | 0 |
| 1 | 3 |
| 2 | 12 |
| 3 | 27 |
What this lesson covers
What you do
You shape the function y = (3*x^2 + 2*x - 5) + (x^2 - 3*x + 7) - (k*x^2 - x + 2) and watch the graph answer.
Challenges to clear
- Combine the like terms: 3x² + x² = 4x². Slide k to 4 — the difference becomes 0 at x = 2.
- Identity confirmed: 0 at x = −1 too. The whole sum is 4x² − x + 2.
- Add the two polynomials. The x² terms combine to 5 + 2 — slide k to 7.
- Now the x terms: 4 and −6. Slide m until the difference is 0 at x = 2 — like terms add, unlike terms never touch.
Check yourself
When adding 3x² + 2x − 5 and x² − 3x + 7, which terms can be combined?
What is (3x² + 2x − 5) + (x² − 3x + 7)?
- 3x² with x², and 2x with −3x — like terms share the same variable AND power. — correct
- 3x² with 2x, because both have an x.
- Only the plain numbers −5 and 7.
- None — polynomials cannot be added.
- 4x² − x + 2 — correct
- 4x² + x + 2
- 3x² − x + 2
- 4x⁴ − x + 2
Think about it
- Like terms: 3x² + x² = ?