BELLWORK Factor a 9 n 2 42 n

BELL-WORK Factor: (a) 9 n 2 – 42 n + 49 = (3 n – 7)2 (b) 27 w 2 – 12 = 3(3 w + 2)(3 w – 2) (c) 3 n 3 – 12 n 2 + 2 n – 8 = (3 n 2 + 2)(n – 4) (d) 9 r 2 + 3 r – 30 = 3(r + 2)(3 r – 5) (e) 30 g 5 + 24 g 3 h – 35 g 2 h 2 – 28 h 3 = (6 g 3 – 7 h 2)(5 g 2 + 4 h) (f) Eureka Module 4 Lesson 3 Problem Set 14 (a 2 – 4)(a 2 – 1) = (a + 2)(a – 2)(a + 1)(a – 1) • Eureka Module 4 Lesson 4 Problem Set 1 i (e) 2 x(3 x + 2)(x – 1) (f)

Area Problems The area of a rectangular computer screen is 4 x 2 + 20 x + 16. The width of the screen is 2 x + 8. What is the length of the screen? 4 x 2 + 20 x + 16 = 4(x + 4)(x + 1) Since one of the stated factors is 2 x + 8, we rewrite this as: = (2 x + 8)(2 x + 2) So the other length is 2 x + 2

Area Problems The area of a rectangular granite countertop is 12 x 2 + 10 x – 12. The width of the countertop is 2 x + 3. What is the length of the countertop? 12 x 2 + 10 x – 12 = 2(2 x + 3)(3 x – 2) Since one of the stated factors is 2 x + 3, we rewrite this as: = (2 x + 3)(6 x – 4) So the other length is 6 x – 4

Area Problems The area of a rectangular book cover is 4 x 2 – 6 x – 40. The width of the book cover is 2 x – 8. What is the length of the book cover? 4 x 2 – 6 x – 40 = 2(2 x + 5)(x – 4) Since one of the stated factors is 2 x – 8, we rewrite this as: = (2 x – 8)(2 x + 5) So the other length is 2 x + 5

Perimeter & Area Problems The function x 2 + 13 x – 48 represents the area of a rectangle. Give an expression for the perimeter of the rectangle. x 2 + 13 x – 48 = (x + 16)(x – 3) Dimension 1 = x + 16 Dimension 2 = x – 3 Perimeter = x + 16 + x – 3 = 4 x + 26

Factoring Polynomials The area of a rectangle can be represented by 2 x 2 + 3 x + 1. Give expressions for the possible length and width of the rectangle. 2 x 2 + 3 x + 1 2 x 2 + 2 x + 1 2 x(x + 1) + 1(x + 1)(2 x + 1) Possible length and width: x + 1 and 2 x + 1

Volume Problems The volume of the rectangular prism is given below. Find expressions for the possible dimensions of the rectangular prism. V = 3 y 3 + 14 y 2 + 8 y = y(3 y + 2)(y + 4) Possible dimensions are: y 3 y + 2 y+4