Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Algebra 2 · Chapter 3 · Lesson 2

Practice Worksheet

Dividing Polynomials

Long division, and the shortcut that replaces it.

11 problems · about 23 minutes · A-APR.B.2, A-APR.D.6

NameDate

Figure — use these to answer the problems

A root is where the curve crosses. Each one corresponds to a factor.

y = 1x³ − 4x + 0

a1

b-4

c0

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

f(x) = x² + 2, divided by (x − 3). Remainder?
Answer
f(x) = x² − 5, divided by (x − 2). Remainder?
Answer
f(x) = x³, divided by (x − 1). Remainder?
Answer
f(x) = x² − 9, divided by (x − 3). Remainder?
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

Is (x − 3) therefore a factor of x² − 9? 1 for yes, 0 for no.
Answer
f(x) = 2x + 6, divided by (x + 3). Remainder?
Answer
Degree 5 divided by degree 2. What is the degree of the quotient?
Answer

Stretch Yourself

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

4 problems

f(x) = x² + x, divided by (x − 2). Remainder?
Answer
9
Select every statement that follows from f(a) = 0.
- (x − a) is a factor.
- a is a root.
- The polynomial has degree 1.
- a is the only root.
- Tick every box that applies.
The Remainder
f(x) = x² + 1 divided by (x − 3). What is the remainder?
Answer
The Factor
f(4) = 0. Is (x − 4) a factor? 1 for yes, 0 for no.
Answer