Use the process you developed in problem 4-13 to factor the following quadratic expressions.

1. $x^2-4x-12$ 

   Hint (a):

   Fill in the rest of the diagram. Remember that the product of the diagonals must be equal.

   Interior boxes of Generic rectangle labeled as follows: top left, negative 6,x, top right, negative 12, bottom left, X squared, bottom right, 2,x. Diamond problem: Left, negative 6,x, Right, 2,x, Top, negative 12 x squared, Bottom, negative 4 x.

   Answer (a):

   Labels added to generic rectangle: Left side, top, negative 6, left side, bottom, x, Bottom side, left, x, bottom side, right, 2.

   $(x−6)(x+2)$

   

   

2. $4x^2+4x+1$ 

   Hint (b):

   Interior boxes of Generic rectangle labeled as follows: top left, blank, top right, 1, bottom left, 4, X squared, bottom right, blank. Diamond problem: Left, blank, Right blank, Top 4, x squared, Bottom 4 x.

   Fill in the rest of the diagram.

   Labels added: Generic rectangle, interior top left, 2,x, interior bottom right, 2,x. Diamond problem: left, 2,x, right, 2,x.

   Answer (b):

   Labels added to rectangle, left side top, 1, left side bottom, 2,x, bottom side left, 2,x, bottom side right, 1.

   $(2x+1)^2$

   

   

   

3. $2x^2-9x-5$ 

   Hint (c):

   Interior boxes of Generic rectangle labeled as follows: top left, blank, top right, negative 5, bottom left, 2, X squared, bottom right, blank. Diamond problem: Left, blank, Right, blank, Top, negative 10, x squared, Bottom, negative 9 x.

   

4. $3x^2+10x-8$