Lesson 11 of 48
Polynomials and roots
Curves whose shape you can predict before you plot a single point.
A factored polynomial tells you where it crosses zero and what it does far away, without arithmetic. Reading structure straight off an expression is the habit that makes later mathematics fast instead of grinding.
Do this
Take a polynomial in factored form you have not seen. Sketch it without plotting points: mark every root, state the behaviour far left and far right, then check with a plot.
The question that unlocks the next lesson
What does the factored form (x − 2)(x + 5) tell you immediately?
- AThe curve's maximum value
- BThe curve crosses zero at x = 2 and x = −5
- CThe curve crosses zero at x = −2 and x = 5
- DThe curve never touches the x-axis