Subtracting Polynomials: The Sign Trap
Watch how the minus sign distributes to every term inside the bracket.
Equation
y = (4*x^2 + 3*x - 5) - (2*x^2 - x + 1) - (2*x^2 + 0*x - 6)
Graph
Table
| x | y |
|---|---|
| 0 | 0 |
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
What this lesson covers
What you do
You shape the function y = (4*x^2 + 3*x - 5) - (2*x^2 - x + 1) - (2*x^2 + k*x - 6) and watch the graph answer.
Challenges to clear
- The sign trap: subtracting −x ADDS x, so 3x − (−x) = 4x. Slide k to 4 — difference 0 at x = 2.
- Still 0 at x = 3 — the minus distributed to every term.
- Subtract the second polynomial from the first. The x² terms give 5 − 1 — slide m to 4.
- Now the sign trap: 2x − (−3x) ADDS to 5x, it does not give −1x. Slide k until the difference is 0 at x = 2.
Check yourself
Why did the term '-x' in the second polynomial become '+x' in the simplified answer?
- Because subtracting a negative is adding a positive — correct
- Because x is always positive
- Because the brackets were removed
- It was a mistake in the simplification
Think about it
- What is 3x minus (−x)?