The rectangle below has a area x^2-x-72 square meters and a length of x+8 meters what expression represents the width of the rectangle

The answer is:

The expression that represents the width of the rectangle is:

We know that the area of a rectangle is equal to:

We are given the function that represents the area of the rectangle and one of its sides, the length is equal to (x+8)

So, rewriting we have:

The coefficients of the variables of the given function are:

Now, to find the width, we need to find two numbers which its product gives as result "-72" and its addition gives as result the coefficient of the linear term of the function (x), its "-1".

Then,

We know that,

So, the factors of the given function are:

Since, we already know that the length corresponds to "x+8", we know that the width corresponds to "x-9".

Proving that the factors are right,

Applying the distributive property, we have:

Hence, the equation is satisfied and we can conclude that:

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