Cogito
AP Precalculus · Chapter 1 · Lesson 3
Polynomials of Degree n
What the leading term decides.
11 problems · about 22 minutes · AP Precalculus 1.6, 1.7
Figure — use these to answer the problems
Warm Up
Straightforward practice. Get the method working first.
4 problemsDegree 8. Maximum turning points?
AnswerDegree 6. Maximum turning points?
AnswerDegree 4. Maximum real zeros?
AnswerMatch each polynomial to its end behaviour.
Draw a line from each item on the left to its match on the right.
- x³
- −x³
- x⁴
- −x⁴
- Down on the left, up on the right
- Up on the left, down on the right
- Up at both ends
- Down at both ends
Build It Up
The same ideas with more to keep track of.
3 problemsDegree 7 with a negative leading coefficient. Does the right end rise? 1 for yes, 0 for no.
AnswerMinimum real zeros of a degree 4 polynomial?
AnswerSelect every polynomial whose ends go in opposite directions.
- x⁵ − x
- x² + 1
- −3x³
- 2x⁶
- Tick every box that applies.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsDegree 2. Maximum turning points?
AnswerWhich term decides end behaviour? Give the degree of that term for 5x⁴ + 9x⁷ − 2.
AnswerTurning Points
A degree 5 polynomial has at most how many turning points?
AnswerThe Guaranteed Zero
How many real zeros must a degree 3 polynomial have at minimum?
Answer