Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
Learning Objecves for CH 2.5 Apply the Remainder And Factor Theorem • Dividing Polynomials
August 30, 2012
Apply the Remainder and Factor Theorems
In earlier sections we have added, subtracted and multiplied polynomials. In this section we are going to divide polynomials. We will use polynomial long division or synthetic division
• Remainder Theorem • Factor Theorem
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Polynomial Long Division
Divide:
by
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
1
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
August 30, 2012
Apply the Remainder and Factor Theorems
OR
OR
Jun 289:25 PM
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Apply the Remainder and Factor Theorems
Remainder Theorem
Factor Theorem
If a polynomial f(x) is divided by xk, then the remainder r = f(k). In the last problem, the function was divided by x3 and the remainder was zero, so f(3)= 0.
A polynomial f(x) has a factor xk, if and only if f(k)=0. In the last problem, the function possessed a factor x3 because f(3)= 0.
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Divide:
Jun 289:25 PM
by
Jun 289:25 PM
2
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
August 30, 2012
Jun 289:25 PM
Apply the Remainder and Factor Theorems
OR
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Divide:
by
OR
Jun 289:25 PM
Jun 289:25 PM
3
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
August 30, 2012
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Synthetic Division
Divide:
by Bring down the one.
Multiply 3 times one
Add 2 and 3 to get positive 1
Jun 289:25 PM
Jun 289:25 PM
4
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
August 30, 2012
Apply the Remainder and Factor Theorems
Multiply 3 times 1 to get 3 again. Then add 3 to 23
Multiply 3 times 20 to get 60. Then add 60 to 60 to get zero.
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
From synthetic division, you get:
Learning Objecves for CH 2.5 Apply the Remainder And Factor Theorem Now factor the second term:
• Dividing Polynomials • Remainder Theorem • Factor Theorem
Jul 95:44 PM
Jun 289:25 PM
5
Learning Objecves for CH 2.5 Apply the Remainder And Factor Theorem • Dividing Polynomials
August 30, 2012
Apply the Remainder and Factor Theorems
In earlier sections we have added, subtracted and multiplied polynomials. In this section we are going to divide polynomials. We will use polynomial long division or synthetic division
• Remainder Theorem • Factor Theorem
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Polynomial Long Division
Divide:
by
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
1
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
August 30, 2012
Apply the Remainder and Factor Theorems
OR
OR
Jun 289:25 PM
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Apply the Remainder and Factor Theorems
Remainder Theorem
Factor Theorem
If a polynomial f(x) is divided by xk, then the remainder r = f(k). In the last problem, the function was divided by x3 and the remainder was zero, so f(3)= 0.
A polynomial f(x) has a factor xk, if and only if f(k)=0. In the last problem, the function possessed a factor x3 because f(3)= 0.
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Divide:
Jun 289:25 PM
by
Jun 289:25 PM
2
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
August 30, 2012
Jun 289:25 PM
Apply the Remainder and Factor Theorems
OR
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Divide:
by
OR
Jun 289:25 PM
Jun 289:25 PM
3
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
August 30, 2012
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Synthetic Division
Divide:
by Bring down the one.
Multiply 3 times one
Add 2 and 3 to get positive 1
Jun 289:25 PM
Jun 289:25 PM
4
Algebra 2 Ch 2.5 Apply the Remainder and Factor Theorems.notebook Apply the Remainder and Factor Theorems
August 30, 2012
Apply the Remainder and Factor Theorems
Multiply 3 times 1 to get 3 again. Then add 3 to 23
Multiply 3 times 20 to get 60. Then add 60 to 60 to get zero.
Jun 289:25 PM
Apply the Remainder and Factor Theorems
Jun 289:25 PM
Apply the Remainder and Factor Theorems
From synthetic division, you get:
Learning Objecves for CH 2.5 Apply the Remainder And Factor Theorem Now factor the second term:
• Dividing Polynomials • Remainder Theorem • Factor Theorem
Jul 95:44 PM
Jun 289:25 PM
5
