CPM Homework Help : AC Problem 8-16

CPM Homework Banner

Home > AC > Chapter 8 > Lesson 8.1.2 > Problem 8-16

8-16.

Use the process you developed in problem 8-13 to factor the following quadratics, if possible.

$x^2-4x-12$
Hint 1(a):
Use a generic rectangle and a diamond to factor the quadratic. Blank Diamond Problem. Draw a rectangle and divide it into four equal parts.
Hint 2(a):
Added to the diamond problem: Left blank, Right blank, Top negative 12 x squared, Bottom negative 4 x. Added to the rectangle: Interior upper right box is negative 12. Interior lower left box is X squared.
Fill in boxes (a):
Added to the diamond problem: Left negative 6 x, Right 2 x. Added to the rectangle: Interior upper left box is negative 6, X. Interior lower right box is 2, X.
Answer (a):
Added to the rectangle exterior: The left edge top is negative 6. The left edge bottom is X. The bottom edge left is X. The bottom edge right is 2. $(x−6)(x+2)$

$4x^2+4x+1$
Hint 1(b):
See the hints in part (a). Blank Diamond Problem. Draw a rectangle and divide it into four equal parts.
Hint 2(b):
Added to the diamond problem: Left blank, Right blank, Top 4, x squared, Bottom 4, x. Added to the rectangle: Interior upper right box is 1. Interior lower left box is 4, X squared.
Fill in boxes (b):
Added to the diamond problem: Left 2, x, Right 2, x. Added to the rectangle: Interior upper left box is 2, X. Interior lower right box is 2, X.
Answer (b):
Added to the rectangle exterior: The left edge top is 1. The left edge bottom is 2, X. The bottom edge left is 2, X. The bottom edge right is 1.
$(2x+1)^2$

$2x^2-9x-5$
Hint (c) and (d):
See the hints in part (a). Blank Diamond Problem. Draw a rectangle and divide it into four equal parts.
Hint (c):
Added to the diamond problem: Left blank, Right blank, Top negative 10, x squared, Bottom negative 9, x. Added to the rectangle: Interior upper right box is negative 5. Interior lower left box is 2, X squared.

$3x^2+10x-8$

© 2022 CPM Educational Program. All rights reserved.