Question

The area of a rectangular room is given by the trinomial x + 3x - 28. What are the possible

Answer 1

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:$x^{2} + 3x - 28$

Now, Area of the rectangle =  Length x Width

Hence, to find the dimensions, we need to factorize the given trinomial.

So, $x^{2} + 3x - 28 = x^{2} + 7x - 4x- 28$

⇒$x^{2} + 7x - 4x- 28 = x(x+7)-4(x+7) = (x+7)(x-4)$

⇒$x^{2} + 3x - 28 = (x+7)(x-4)$

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).