p. 610 4, 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 factor2. Patterns:

▪ Difference of Squares: a2 – b2 = (a – b)(a + b)

▪ Perfect Square Trinomial: a2 + 2ab + b2 = (a + b)2

▪ Perfect Square Trinomial: a2 - 2ab + b2 = (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)

2y2(y - 5) – 3(5 – y) Are y – 5 and 5 – y the same thing? No, but –(5 - y) = -5 + y = y - 5 Now 2y2(y - 5) – 3(5 – y) = 2y2(y - 5) +

3(y - 5) (2y2 + 3)(y – 5)

x3 +2x2 + 8x + 16 The first two terms have an x2 in

common; the two last terms have 8 in common.

x2 (x+ 2) + 8(x + 2) (x2 + 8)(x + 2) Can you break this down any further?

r2 +4r + rs + 4s r( r + 4) + s(r + 4) (r + s) (r + 4)

r2 +4r + 4s + rs r(r + 4) + s(4 + r) (r + s)(r + 4)

r2 + rs + 4r + 4s r(r + s) + 4(r + s) (r + 4)(r + s)

Any way you group this one, it comes out the same.

x3 -10 – 5x + 2x2

(x + 2)(x2 – 5)

x2 – 4x -3

Prime!

3x3 – 21x2 – 54x

3x(x + 2)(x – 9)

8d3 + 24d

8d(d2 + 3)

A kitchen drawer has a volume of 768 in3. If the dimensions are as shown, what are the length, width, and height of the drawer?

(w)(w + 4)(16 – w) = 768 -w3 + 12w2 + 64w – 768 = 0 -w2(w - 12) + 64(w – 12) = 0 (-w2 + 64)(w – 12) = 0 Possible Solutions: w = 8 (12, 8) or w = 12 (4,

16)

w w + 4

16- w