P. 610 4, 10, 12, 15, 17, 20, 24, 27, 31, 36, 40, 44, 47, 56, 59, 60, 62, 70, 76.

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p , 10, 12, 15, 17, 20, 24, 27, 31, 36, 40, 44, 47, 56, 59, 60, 62, 70, 76

Objective: factor polynomials completely including grouping methods

1. GCF: greatest common factor 2. Patterns: ▪ Difference of Squares: a 2 – b 2 = (a – b)(a + b) ▪ Perfect Square Trinomial: a 2 + 2ab + b 2 = (a + b) 2 ▪ Perfect Square Trinomial: a 2 - 2ab + b 2 = (a - b) 2 3. “un-FOIL” 4. Grouping: What we’re doing today!

 4x(x -3) + 5(x-3)  We have 4x + 5 of the (x-3)’s.  Another way to write it: (4x + 5)(x-3)  2y 2 (y - 5) – 3(5 – y)  Are y – 5 and 5 – y the same thing?  No, but –(5 - y) = -5 + y = y - 5  Now 2y 2 (y - 5) – 3(5 – y) = 2y 2 (y - 5) + 3(y - 5)  (2y 2 + 3)(y – 5)

 x 3 +2x 2 + 8x + 16  The first two terms have an x 2 in common; the two last terms have 8 in common.  x 2 (x+ 2) + 8(x + 2)  (x 2 + 8)(x + 2)  Can you break this down any further?

 r 2 +4r + rs + 4s  r( r + 4) + s(r + 4)  (r + s) (r + 4)  r 2 +4r + 4s + rs  r(r + 4) + s(4 + r)  (r + s)(r + 4)  r 2 + rs + 4r + 4s  r(r + s) + 4(r + s)  (r + 4)(r + s)  Any way you group this one, it comes out the same.

 x – 5x + 2x 2  (x + 2)(x 2 – 5)  x 2 – 4x -3  Prime!  3x 3 – 21x 2 – 54x  3x(x + 2)(x – 9)  8d d  8d(d 2 + 3)

 A kitchen drawer has a volume of 768 in 3. If the dimensions are as shown, what are the length, width, and height of the drawer?  (w)(w + 4)(16 – w) = 768  -w w w – 768 = 0  -w 2 (w - 12) + 64(w – 12) = 0  (-w )(w – 12) = 0  Possible Solutions: w = 8 (12, 8) or w = 12 (4, 16) w w w