03 Long Division.notebook
March 10, 2014
Methods of Factoring
1. GCF
always look for a common number that all the numbers of the polynomial divide into that can be factored out.
always look to see if all of the terms have an "x" that can be factored out.
2. Difference of 2 Squares
• binomial
• minus sign
• square terms
Methods of Factoring
Methods of Factoring
3. UnFOIL
• trinomial
• signs read: same/both or different/bigger
• Factors of (first*last) that +/­ to middle
4. Perfect Trinomial Square (Butterfly)
• trinomial
• last sign MUST be positive
• 1st & last terms are squares
• Butterfly test works
Methods of Factoring
1
03 Long Division.notebook
March 10, 2014
Factor:
answers
1. 8x ­ 20
2. x2 + 10x + 16
3. 16x2 ­ 24x + 9
4. x2 + 10x
5. 9x2 ­ 49
6. 2x2 + 8x + 8
Factor
1. 8x ­ 20
Factor:
2. x2 + 10x + 16
UnFOIL
GCF Method
(x + 8)(x + 2)
4(2x - 5)
3. 16x2 ­ 24x + 9
4. x2 + 10x
Butterfly Method
GCF Method
(4x - 3)(4x - 3)
5. 9x2 ­ 49
(x + 10)
6. 2x2 + 8x + 8
Difference of 2 Squares
(3x - 7)(3x + 7)
GCF & Butterfly
2(x + 2)(x + 2)
Answers
2
03 Long Division.notebook
March 10, 2014
Simplifying Rational Expressions
1. Factor!
2. Factor!
3. FACTOR!
4. FACTOR some more!!!
5. Cancel like sums because canceling parts of sums is the ultimate sin in
mathematics!!!
Let's make some corrections!!
Get out Worksheets 11-1 & 11-2
Simplifying Rational Expressions
True or False??
True
True
True
True
NOTE: To simplify a polynomial divided by a
monomial, divide each term in the
numerator with the denominator
Poly divided by Mono
3
03 Long Division.notebook
March 10, 2014
Divide:
Long Division Vocabulary:
Divisor ­ the polynomial outside the division sign
(the denominator)
Dividend ­ the polynomial inside the division sign
(the numerator)
Quotient ­ The answer (including remainder)
Long Division
Steps for Polynomial Long Division
1. Write the polynomials in descending order. Make the countdown complete by filling in any
missing terms.
2. Divide first term of dividend by the first term of the divisor. Write the answer up top.
3. Multiply answer by entire divisor and write under the corresponding terms of the dividend.
4. Change all of the signs of the terms found from step 3 and combine.
5. Bring down the next term of the divisor and repeat steps 2 - 5 until done.
Steps for Polynomial Long Division
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03 Long Division.notebook
March 10, 2014
Simplify using Long Division
x+ 6
x2+ 6x
6x + 36
6x + 36
Example 1
Simplify using Long Division
x -7 r1
2x2 + 3x
-14x - 20
-14x - 21
1
Example 2
5
03 Long Division.notebook
March 10, 2014
Simplify using Long Division
x - 3 r 18
+ 0x
x2 + 3x
-3x + 9
-3x - 9
18
Example 3
Simplify using Long Division
x - 1 r -48
x2 + 1x
-1x - 49
-1x - 1
-48
Example 4
6
03 Long Division.notebook
March 10, 2014
Homework:
Worksheet 11-3
Quiz Next
Class
Homework
7