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8-17.

Use the process you developed in problem 8-14 to factor the following quadratics, if possible.

  1. Use a generic rectangle and a diamond to factor the quadratic.  Blank Diamond Problem. Draw a rectangle and divide it into four equal parts.

    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.

    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.

    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.

  1. See the hints in part (a). Blank Diamond Problem. Draw a rectangle and divide it into four equal parts.

    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.

    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.

    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. 

  1. See the hints in part (a). Blank Diamond Problem. Draw a rectangle and divide it into four equal parts.

    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.