Answer:
The possible dimensions of the rectangle are (x+7) and (x -4).
Step-by-step explanation:
Here, the given expression for area of the rectangle is:[tex]x^{2} + 3x - 28[/tex]
Now, Area of the rectangle = Length x Width
Hence, to find the dimensions, we need to factorize the given trinomial.
So, [tex]x^{2} + 3x - 28 = x^{2} + 7x - 4x- 28[/tex]
⇒[tex]x^{2} + 7x - 4x- 28 = x(x+7)-4(x+7) = (x+7)(x-4)[/tex]
⇒[tex]x^{2} + 3x - 28 = (x+7)(x-4)[/tex]
So, the factors of the polynomial are (x+7) and (x -4)
Hence, the possible dimensions of the rectangle are (x+7) and (x -4).
