ON TARGET Algebra Tiles ON TARGET Adding Polynomials

ON TARGET Algebra Tiles

ON TARGET Adding Polynomials -1 xxxxx 1 -x -x 1 1 1 xxx 1

ON TARGET Adding Polynomials (Find the Perimeter)

ON TARGET Subtracting Polynomials -1 xxxxx -11 x -x 1 -1 -11 xxx xx xx -1 -1

ON TARGET Subtracting Polynomials You Try!

ON TARGET Factoring out the GCF x x x 1 1 1 Graphic Organizer X + 1+ 1 x x x 1 1 1 1 +1 1 x x 1 1 1 1 3 groups of x+2 X +2 x + x 3 x 6+6 x 3

ON TARGET Factoring out the GCF

ON TARGET Factoring out the GCF -x -x -x x-2 -3 1 1 1 Graphic Organizer x -1 -1 -1 -x x -11 -1 -x x -1 1 -1 x -x 1 -1 -x -x -x -3 -3 x +6

ON TARGET Factoring out the GCF

ON TARGET Factoring out the GCF -x -x

ON TARGET Factoring out the GCF X x +X x -1 -1 Graphic Organizer x x -x +x x -x 2 x -x -x

ON TARGET Factoring out the GCF -x -x -x

ON TARGET Factoring out the GCF x x -1 -1 -x -x Graphic Organizer +x -x -x 3 x

ON TARGET Factoring out the GCF

ON TARGET Factoring out the GCF x Graphic Organizer 2 2 x x 3 x

ON TARGET Factoring out the GCF

ON TARGET Factoring out the GCF

ON TARGET Multiplying Polynomials

ON TARGET Multiplying Polynomials Graphic Organizer Algebra Tiles or Area Model (x + 1)(x + 2) x +1 +1 x x 2 x x +1 x 1 1 x +2 x xx 22 +x 2 x x +1 +xx +2 x 2 + 2 x + 2 x 2 + 3 x + 2 (x + 1)(x + 2) Multiplying Binomials x 2 + 3 x + 2 Mnemonic Device: FOIL F +O +I +L (x + 1)(x + 2) x 2 + 2 x + 2 x 2 + 3 x + 2

ON TARGET Checking your work

ON TARGET Multiplying Polynomials Algebra Tiles or Area Model Graphic Organizer (x + 2)( x + 3) x x +1 +1 +1 x 2 x x x +2 x xx 22 +x 2 x x +3 + xx 3 x x +6 +1 +1 1 1 1 x 2 + 3 x + 2 x + 6 x 2 + 5 x + 6 x x 2 + 5 x + 6

ON TARGET Checking your work

ON TARGET Multiplying Polynomials You Try!

ON TARGET Multiplying Polynomials Algebra Tiles or Area Model Graphic Organizer (x – 3)(x + 1) x x x +1 x xx 22 +x x -3 -3 x -x -3 +1 x 2 x -1 -x -1 -1 -1 -x -1 x 2 – 3 x + x − 3 x 2 – 2 x – 3 -x x 2 – 2 x – 3

ON TARGET Checking your work

ON TARGET Multiplying Polynomials You Try!

ON TARGET Algebra Tiles Make a Rectangle x + 2 x x + + 1 1 x + 2 x x + + 3 3 x + 2

ON TARGET Multiplying Polynomials Algebra Tiles or Area Model Graphic Organizer (x – 3) x x -1 -1 -1 x 2 -x -x -x -1 -1 -1 -x -x -x 1 1 1 1 1 x -3 x xx 22 -x-3 x -x -x -3 -3 x -x -9 -x x 2 – 6 x + 9 This trinomial is also a Perfect Square. By definition, a square has all sides equal. (x – 3)2

ON TARGET Multiplying Polynomials You Try! Draw the algebra tiles

ON TARGET Multiplying Polynomials

ON TARGET Factoring Polynomials

x 2 x xx ON TARGET Factoring Polynomials 1 1 1 Now arrange them to make a rectangle

ON TARGET Factoring Polynomials Graphic Organizer x x + 3 x + 2 x x x +1 +1 +1 +2 x xx 22 +x 2 x x +3 + xx 3 x x +6 +1 +1 x 2 x x 1 1 1 x

ON TARGET Alternate Route ? ? ? x 2 + 2 x ? + 3 x +6

ON TARGET Factoring Polynomials You Try!

ON TARGET

ON TARGET Factoring Polynomials x 2 -1 -1 Now arrange them to make a square

Remember there were no middle terms … x 2 -x -x x x -1 -1 Use zero pairs! 4 empty spaces = 2 zero pairs x x + 2 Graphic Organizer - 2 -1 -1 x -x -x x 2 -x -x x ON TARGET Factoring Polynomials +1 +1 x x -1 -1 x -2 x xx 22 -2 x x x +2 x xx -4

-1 -1 -1 x x 2 x Now try to arrange them to make a rectangle -1 -1 -1 x 2 x ON TARGET Factoring Polynomials -1 -1 -1 When you have an even number of x’s missing use zero pairs

x -x -x x x -1 -1 -1 x 2 -x x x x 2 -x -x x -x -x x ON TARGET x -x -x -1 -1 -1

ON TARGET Factoring Polynomials Algebra Tiles or Area Model Graphic Organizer x x -1 -1 1 1 x +3 x xx 22 x+3 x xx -2 -2 x -x -6 1 x 2 x x x -x -x 1 1 1 (x – 2)(x + 3)

ON TARGET Alternate Route ? ? x 2 ? + 3 x ? +6

ON TARGET Factoring Polynomials You Try!

Now try to arrange them to make a rectangle -1 -1 x x -1 -1 Not an even number of missing x’s… can’t use zero pair x -1 +1 +1 +1 x 2 xxx x x 2 +1 -x -1 -1 When you have an even number of x’s missing use zero pairs xx x 2 xxx ON TARGET Factoring Polynomials

ON TARGET Factoring Polynomials Draw the algebra tiles You Try!

x 2 xxxxx ON TARGET Factoring Polynomials -1 -1 -1

x + 3 x x +1 +1 +1 x x 2 xxx X+ x 2 xxx -1 x- ON TARGET Factoring Polynomials -1 -1 -1 +3 2 x -1

ON TARGET ? Alternate Route ? ?

ON TARGET

ON TARGET Factoring Polynomials You Try! Draw the algebra tiles

ON TARGET Completing the Square

Let’s make a square with the given tiles Now place the length of 8 Since tiles split into 2 x each yellow tiles side is x+4, to two groups complete square it! the x xxx square! x 2 x x xxxx ON TARGET Completing the Square 1 1 1 1 16 Yellow tiles

ON TARGET Factoring Polynomials You Try! Draw the algebra tiles