Answer:
The factor form of given expression is [tex](x-7)(x+4)[/tex].
Step-by-step explanation:
The given expression is
[tex]x^2-3x-28[/tex]
[tex]x^2-7x+4x-28[/tex]
[tex]x(x-7)+4(x-7)[/tex]
[tex](x-7)(x+4)[/tex]
Therefore the factor form of given expression is [tex](x-7)(x+4)[/tex].
If a expression is in the form of [tex]ax^2+bx+c[/tex], then in X diagram ac is written on the top, b is written on the bottom and the required factors of ac are written on the sides.
In the given expression,
[tex]a=1[/tex]
[tex]b=-3[/tex]
[tex]c=-28[/tex]
[tex]ac=1\times -28=-28[/tex]
The X diagram is shown in the given figure.
Therefore the factor form of given expression is [tex](x-7)(x+4)[/tex].
We need to factorize the given equation to identify the values that should be written to complete the X diagram.
The values written to complete the X diagram. On top -28, On the bottom: -3 and On the sides: -7 and 4.
Given:
The given equation is [tex]x^2-3x-28[/tex].
Consider the given equation.
[tex]x^2-3x-28[/tex]
Find the factor of the above equation.
[tex]x^2 -7x +4x -28\\ x(x -7) +4(x -7)\\ (x +4)(x -7)[/tex]
Consider the general equation.
[tex]ax^2+bx+c[/tex]
In X diagram, we can write [tex]ac[/tex] on the top, [tex]b[/tex] on the bottom and the required factors of [tex]ac[/tex] are the sides.
Compare the above expression.
[tex]a=1\\b=-3\\c=-28\\ac=-28[/tex]
Thus, the values written to complete the X diagram. On top -28, On the bottom: -3
The X diagram shown below.
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