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Cogito

Algebra 2 · Chapter 3 · Lesson 1

Practice Worksheet

Polynomial Behaviour and the Factor Theorem

What the degree tells you before you draw anything.

10 problems · about 21 minutes · A-APR.B.2, A-APR.B.3, F-IF.C.7

NameDate

Figure — use these to answer the problems

A cubic has ends going opposite ways. Flip the leading coefficient and watch them swap.
-8-8-6-6-4-4-2-222446688
y = 1x³ − 3x + 0
  • Point(2, 2)
Leading coefficient1
Linear coefficient-3
Constant0
Read at x2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “The Quadratic Formula and the Discriminant”

    x² + 3x + 2 = 0. What is the discriminant?

    Answer

  2. From “Arithmetic with Complex Numbers”

    (4 + 3i)(4 − 3i). Result?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. f(x) = x² − 9. What is f(3)?

    Answer

  2. What does the Factor Theorem say?

    • f(a) = 0 exactly when (x − a) is a factor.
    • The degree equals the number of factors.

  3. Maximum roots of a degree 4 polynomial?

    Answer

  4. f(x) = x² − 5x + 6. What is f(2)?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. f(x) = x³ − 8. What is f(2)?

    Answer

  2. Do the ends of an odd-degree polynomial go the same way?

    • No. Opposite ways.
    • Yes.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Degree

    How many roots can a degree 5 polynomial have at most?

    Answer

  2. The Test

    f(x) = x³ − 7x + 6. What is f(1)?

    Answer