Dr
aft
DO NOW
1
Take out your homework from the previous lesson.
2
Prepare any notebook paper you may need for today’s
lesson. The lesson title is “Factor/Remainder Theorems”.
Today’s date is Oct. 24,2014.
3
NEWS: Any slide in lecture that has a F symbol on it
means you should put the work IN YOUR NOTES (not
on the slides, not on the DO NOW organizer). Make
corrections as we go over the problems.
4
Label the first part of today’s notes “Warm-up” and
complete the Warm-up problems on the next slide.
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
Warm-Up
Dr
aft
F
4
What is remainder in
problem 1?
x + 3 ) x 2 − 4x − 21
5
What is p(−3) if
p(x) = x 2 − 4x − 21?
x − 5 ) x3
6
What is p(5) if
p(x) = x 3 + 4x − 272?
1
6 ) 1872
2
3
+ 4x − 272
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
3 The Remainder Theorem
F
2
Dr
aft
p(x) = x 3 + 8x − 2
1 evaluate p(3).
Use synthetic division to find the remainder of
David Rennie
p(x)
.
x −3
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
Dr
aft
4 The Remainder Theorem Explained
The Remainder Theorem says . . .
if any polynomial is divided by a linear factor, its remainder
will always be equal to the output given by plugging in the
zero of the same factor.
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
5 Think-Pair-Share
F
Haley
x −7
Dr
aft
Haley and Lillian each prove that (x − 7) is a factor of the
polynomial f (x) = x 3 − 10x 2 + 11x + 70 .
Lillian
x 2 − 3x
x 3 − 10x 2 + 11x
− x 3 + 7x 2
− 3x 2 + 11x
3x 2 − 21x
− 10x
10x
− 10
+ 70
f (x) = x 3 − 10x 2 + 11x + 70
f (7) = (7)3 − 10(7)2 + 11(7) + 70
f (7) = 313 − 490 + 77 + 70
f (7) = 0
+ 70
− 70
0
QUESTION: Why do both methods work?
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
F
Dr
aft
6 Finding More Factors
1
Use Haley’s answer from the previous slide to rewrite f (x)
as a product of (x − 7) and some other polynomial.
2
Look at the polynomial that is not (x − 7). Factor it into
two other factors.
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
F
Dr
aft
7 Challenge Problem
You are given the polynomial
f (x) = 2x 4 + x 3 − 14x 2 − ax − 6
and are told that (x − 3) is a factor of the polynomial.
What number would a have to be in order to make this
statement true?
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)
Proving Behavior: Alg2 (Oct. 24,2014)
Dr
aft
Marcus claims that (x + 2),(x − 3),(x + 1),and(x − 2) are all
factors of x 4 − x 3 − 7x 2 + x + 6. Is he correct? Justify your
answer.
David Rennie
Alg 2: Factor/Remainder Theorems(Oct. 24,2014)