

Remainder and Rational Root Theorem
Presentation
•
Mathematics
•
9th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
9 Slides • 7 Questions
1
2.5 Factor and Remainder
Theorem
●Explain why when (x-k) is a factor of a polynomial, x=k is a zero of the
polynomial
●Interpret the remainder of a polynomial divided by (x-k)
●Given one factor of a polynomial function, use division to find the remaining
factors
2
3
4
5
6
Multiple Choice
What is (x2 + 2x − 15) divided by (x + 5)?
x+2
x+3
x-3
5x−3x2+2
7
Multiple Choice
What is (2x5 - 5x4 + 7x3 +4x2 - 10x + 11) divided by (x3 + 2)
8
Multiple Choice
What is the remainder of (2x3 - x2 - 13x + 9) divided by (x - 2)
-7
-5
7
5
9
10
Let’s check it out:
f(-1) = 3(-1)3+(-1)2+2(-1)+5
f(-1) = -3 + 1 -2 + 5
f(-1) = 1
If there is a
remainder then (-1) is
not a zero of the
polynomial.
11
Multiple Choice
Try it now using the remainder theorem:
What is the remainder of (2x3 - x2 - 13x + 9) divided by (x - 2)
-7
-5
7
5
12
Multiple Choice
If (9x4−45x3+37x2+x+2) is divided by (x−2) then the remainder is...
-64
64
656
-652
13
Multiple Choice
If a polynomial p(x) is divided by x-a, then the remainder is obtained by:
P(-a)
P(a)
P(a/2)
P(-a/2)
14
Multiple Choice
If p(x)=x3−ax2+6x−a is divided by (x−a) , then the remainder is...
5
-5
a
5a
15
16
CYU
2.5 Factor and Remainder
Theorem
●Explain why when (x-k) is a factor of a polynomial, x=k is a zero of the
polynomial
●Interpret the remainder of a polynomial divided by (x-k)
●Given one factor of a polynomial function, use division to find the remaining
factors
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