Warm Up 

no

0, 3

x = -3

 

 

Homework Questions

Section 2.2 Synthetic Division; The Remainder and Factor

TheoremsObjective: To use synthetic division

and to apply the remainder and factor theorems.

Vocabulary

RemainderQuotient DivisorDividend RemainderQuotientDivisorDividend

35423

35423

When 23 is divided by 4, the quotient is 5 and the remainder is 3.

4 is not a factor of 23, because if when 23 is divided by 4 the remainder is not zero.

The Remainder Theorem

When a polynomial P(x) is divided by x – a, the remainder is P(a)

)()( axxP Remainder =P(a)

2-2 Synthetic Division; The Remainder and Factor THMs

4 2Divide 2 15 10 5 by 3x x x x

3 2 0 -15 -10 5

266

183

91

32

4 23 22 15 10 5 2

2 6 3 13 3

x x xx x x

x x

Example 1

Divide P(x) = x3+ 5x2 + 5x – 2, by x + 2

The Factor Theorem

 

if and only if

⇔

Example 4

If P(x) = 2x4 + 5x3 – 8x2 – 17x – 6, determine whether each of the following is a factor of P(x):

A) x – 1

B) x – 2

Example 3

If x = -1 is a root, find all others roots for

p(x)= x3+ 3x2 + x – 1

Classwork

Class ExercisesPage 60 #1-5

Homework

Section 2.2

Page 61 #1-25 odds

√7+√14−15√7

−14 √7+√14

3 𝑖√21−2 𝑖√21−√21(−1−𝑖)√21

8 𝑥 √3+2𝑥 √9−31𝑥 √3

6 𝑥−23𝑥 √3

√31𝑥2+2 𝑥√31+5√31 𝑖

(3 𝑥−5)√31

√8+4 √2−6√50

−24 √2

−2√3−√27+3 √27

4√3

6+3√6

6 √5+15√2

−10+√2

4√72𝑎4𝑏4

24 𝑎2𝑏2 √2