A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
The Remainder Theorem
A.APR.2 A.APR.6
a) Divide g(x) by x+1
b) Evaluate g(­1)
a) Divide h(x) by x­3
b) Evaluate h(3)
a) Divide j(x) by x+2
b) Evaluate j(­2)
A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
a) Divide h(x) by x­3
b) Evaluate h(3)
a) Divide j(x) by x+2
b) Evaluate j(­2)
A2M1L19­SB The Remainder Theorem.notebook
a) Divide g(x) by x+1
October 07, 2015
b) Evaluate g(­1)
A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
What do we notice about these three cases?
What appears to be a general rule about the connection between dividing by (x­a) and the value of P(a)?
Proof of the Remainder Theorem
If: then: and
A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
Practice using the Remainder Theorem
What is the remainder when P(x) is divided by
a) (x+2)?
b) (x+1) ?
A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
The Factor Theorem
If a is a zero of P(x) then x­a is a factor of P(x).
A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
Given: P(x) = x3+2x2­29x+42
1) Verify that P(3) = 0 Since P(3)=0, what must one of the factors of P be?
2) Find the remaining two factors.
3) State the zeros of P
4) Sketch the graph of P
A2M1L19­SB The Remainder Theorem.notebook
October 07, 2015
Homework: Remainder Theorem HW Worksheet