Identify the values that should be written to complete the X diagram.
On the top: –28–31
On the bottom: –28–31
On the sides: –14 and 2–7 and 4–4 and 7

Rewrite the expression using the numbers on the sides of the X diagram.

Use double grouping to factor the four terms.
x2 – 3x – 28 = (x – 14)(x + 2)(x – 7)(x + 4)(x + 7)(x – 4)

See the attachment for what goes on your X diagram.

Rewrite: x² -7x +4x -28

Grouping: (x² -7x) +(4x -28) = x(x -7) +4(x -7) = (x +4)(x -7)

Step-by-step explanation:

The given quadratic is ...

... x² -3x -28 . . . . . a=1, b=-3, c=-28

a) The value at the top of the X diagram is the product a·c = 1·(-28) = -28.

The value at the bottom of the X diagram is the coefficient b = -3.

The values on the sides of the diagram are the factors of -28 that add up to make -3. These are -7 and 4. That is, ...

(-7)·(4) = -28

(-7)+(4) = -3

b) Since the two values on the sides of the diagram add up to give "b", the value of "b" in the equation can be rewritten as the sum of these two numbers. Doing that, we have ...

... x² -3x -28

... = x² +(-7+4)x -28

... = x² -7x +4x -28 . . . . . . order does not matter. It could also be x² +4x -7x -28

c) We can group pairs of terms in the rewritten expression and factor each pair.

... = (x² -7x) +(4x -28) . . . . . first pair has a common factor of x; second pair, 4

... = x(x -7) +4(x -7) . . . . . . . these terms now have a common factor: (x -7)

... = (x +4)(x -7) . . . . . . . . . . the complete factorization of x² -3x -28

a net is a diagram that shows a “flattened” view of a solid. in a net, each face and base is shown with all of its dimensions. a net can also serve as a pattern to build a three-dimensional solid.

a pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.

" the net of a triangular pyramid consists of four triangles. the base here we are given of the pyramid is a equilateral   triangle, and the lateral faces are also triangles "

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