An archeitect is designing a rectangular fountain for the city park. It's area is represented by 16x-40. Factor this binomial to determine the greatest lengh and width measurements that fountain could have?
To factor the given binomial, 16x - 40, we need to find its greatest common factor (GCF) and apply the distributive property.
Step 1: Find the GCF of the coefficients of the binomial, which are 16 and -40. The GCF of 16 and 40 is 8.
Step 2: Rewrite the binomial using the GCF: 8(2x - 5).
Now, by factoring the binomial 2x - 5, we can determine the greatest length and width measurements that the rectangular fountain could have.
The factors of 2x - 5 are (2x - 5) itself, as it is an irreducible binomial.
Therefore, the greatest length measurement of the fountain would be 2x - 5, and the greatest width measurement would also be 2x - 5.