Answer:
A=4.
Step-by-step explanation:
Note: In the expression of area the first term should be [tex]Ax^2[/tex].
It is given that area of a rectangular floor of your house is [tex]Ax^2+5x-2[/tex] and the length is [tex](x+2)[/tex] units.
We know that, area of a rectangle is
[tex]Area=length\times width[/tex]
Since length of the rectangle is [tex](x+2)[/tex], therefore [tex](x+2)[/tex] is a factor of [tex]Ax^2+5x-2[/tex] and the value of [tex]Ax^2+5x-2[/tex] is 0 at x=-2.
[tex]A(-2)^2+5(-2)-2=0[/tex]
[tex]4A-10-2=0[/tex]
[tex]4A-12=0[/tex]
[tex]4A=12[/tex]
Divide both sides by 4.
[tex]A=4[/tex]
Therefore, the value of A is 4.
