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Nov 15:03 PM
5.1 Multiplying Polynomials
Recall Adding Polynomials:
(2g+3b) + (1g+2b)=3g+5b
What happens with(2g+3b) * (1g+2b)?
Nov 110:22 AM
x
1
x
x x2 x2
x x
A=l*w=2x(x+1)=2x^2+2x
Nov 110:22 AM
x
1
x x2
x
x
x1
x
(2x-2)(x-1) =2x^2-2x-2x+22x^2-4x+2Success!!!
x
x2
11
1 1
x
x x
x2
Nov 110:22 AM
x
1
x
x2
x2
xx
11
x x
11
x
1 1
x2 x2
1 1
Nov 110:48 AM Nov 28:41 AM
2
Nov 22:18 PM
2x^2-8xy-xy+4y^2F O I L2x2-9xy+4y2
Nov 29:53 AM
Test Rewrite options:-redo just one section-redo just one learning outcome-redo whole test?!
Before the retest:-finish review-do corrections-tomorrow lunch tutorial
Nov 15:03 PM
5.2 Common Factorsx
1
x
x x2 x2
x x
Nov 15:11 PM
Nov 15:11 PM Nov 29:22 AM
3
Nov 89:45 AM
Cam Jillian
66 23716
2x3x11 2x2x7x7x11x11
2x2x3x7x7x11x11=71148
Nov 82:24 PM
Find the "All-Star" "Dream Team" please-everyone, Mountain High, Super Hero Pizza
1: Crust2: Cheese3: Pepperoni5: Pineapple7: Mushroomsx: "mystery" meaty: "mega mouthwatering mystery" meat
Jasmine: 63x2 Nick: 12xy Gregory: 18x
Nov 29:33 AM Nov 22:09 PM
Nov 29:38 AM Nov 29:52 AM
p. 220 #(1-7, 12)o.l.
4
Nov 22:33 PM
§ 5.3 Factoring Trinomials
x2 x2
x x
x x
11
To factor this expression, set up algebra tiles that give a product of 2x2+4x+2
2x2+4x+2=(x+1)(2x+2)
x
x x 1 1
1
Nov 22:37 PM
x
1
x
xx2
xx
1 1
x x
11
Ex 2: set up tiles for x2+7x+10
xxxx
111111
Nov 22:37 PM
x
1
x
x x2
xx
1 1
x x
11
Ex 2: set up tiles for x2+7x+10
xxxx
111111
11
11111
x2+7x+10=(x+5)(x+2)
Nov 22:37 PM
x
1
x
x x2
x x
1 1
x
x
11
Ex 2: set up tiles for 2x2+3x+1
x
x
xx
111111
1
1 1
1111
x2+7x+10=(x+5)(x+2)
x2
2x2+3x+1=(x+1)(2x+1)
Nov 22:37 PM
x 1x
x x2
x x
1 1
x
x
11
Ex 2b: set up tiles for 3x2+5x-2
x
x
xx
111111
11 1
1111
x2+7x+10=(x+5)(x+2)
x2
x
1
1
x2
x
x
x
x x 1
Nov 32:17 PM
5
Nov 33:03 PM Nov 39:07 AM
Can we do this without algebra tiles?
Ex 1: x2+3x+2=(x+_)(x+_)
Our missing numbers should be integers with a sum of 3 and a product of 2
x2+3x+2=(x+1)(x+2)
Integers Sum Product
1,2 3 2
1,2 3 2
1,4 3 4
1,2 1 2
1,3 4 3
Nov 22:37 PM
Start p. 235: #1-4
Nov 39:07 AM
Ex 2: x2+3x4=(x+_)(x_)
Our missing numbers should be integers with a sum of 3 and a product of -4
x2+3x4=(x+4)(x1)
Integers Sum Product
1,2 3 2
1,2 3 2
1,4 3 4
1,2 1 2
1,3 4 3
Nov 39:07 AM
Ex 3: 2x2+6x8
If all three terms have a common factor, we can deal with this first!
x2+3x4=(x+4)(x1)
Ex 3: 2x2+6x8=2(x2+3x4)
Nov 510:39 AM
The difficult ones:
Ex: factor 2x2+11x+12
try splitting up the middle term to get two binomials that factor nicely :)
2x2+8x+3x+122x(x+4)+3(x+4)(2x+3)(x+4)
6
Nov 510:39 AM
How do you know?
Ex: factor 2x2+11x+12-look for two integers with a sum of 11 and a product of 24!
2x2+8x+3x+122x(x+4)+3(x+4)(2x+3)(x+4)
Mar 1011:12 AM
Mar 1011:14 AM Nov 510:39 AM
Method 3
We know (x+a)(x+b) "foils" to give us x2+(a+b)x+abSo why not try skipping straight to
(x+_)(x+_) when factoring?
Ex: factor x2+5x+6
try writing (x+ )(x+ )now fill in the blanks with an educated guess!
Nov 158:56 AM Nov 152:06 PM
7
Nov 159:04 AM Nov 22:37 PM
Finish p. 235 #1-4, continue #(5-9) o.l.
Nov 410:14 AM
"Perfect" Trinomials
ex 1) x2-4=x2+0x-4
perfect squares
A difference of squares always factors like:(x+2)(x-2)
Mar 149:08 AM
Nov 410:44 AM Nov 410:48 AM
8
Nov 410:50 AM Nov 152:10 PM
Nov 22:40 PM
p. 246 #(1-7) o.l., 14
Nov 22:40 PM
Review: p. 252 #1-2, 6-7, 10-11, 13-15
Oct 33:05 PM