Which of the following endpoints is best suited for using polynomial identities to convert differences of numerical squares into products?(1 point)
1. 8.4 and 11.1
2. 7.2 and 10
3. 8 and 10
4. 8 and 11.5
The best choice for using polynomial identities to convert differences of numerical squares into products would be option 3: 8 and 10.
To determine the best endpoint for using polynomial identities to convert differences of numerical squares into products, we can calculate the differences of the given numbers and see which pair has a difference that can be factored easily using polynomial identities.
1. Difference: 11.1 - 8.4 = 2.7
2. Difference: 10 - 7.2 = 2.8
3. Difference: 10 - 8 = 2
4. Difference: 11.5 - 8 = 3.5
Based on the differences calculated, the pair (3) with endpoints 8 and 10 has the smallest difference of 2, which can be easily factored using polynomial identities.
To determine the best endpoint for using polynomial identities, we need to examine which endpoint pairs have differences that can be easily converted into products using polynomial identities.
The polynomial identity we can use for this problem is the difference of squares identity, which states that for any two numbers a and b, the difference of their squares can be represented as (a - b)(a + b).
Let's calculate the differences of squares for each of the given endpoints:
1. Endpoint 1: The difference of squares for 8.4 and 11.1 would be (11.1)^2 - (8.4)^2 = 123.21 - 70.56 = 52.65
2. Endpoint 2: The difference of squares for 7.2 and 10 would be (10)^2 - (7.2)^2 = 100 - 51.84 = 48.16
3. Endpoint 3: The difference of squares for 8 and 10 would be (10)^2 - (8)^2 = 100 - 64 = 36
4. Endpoint 4: The difference of squares for 8 and 11.5 would be (11.5)^2 - (8)^2 = 132.25 - 64 = 68.25
Based on the calculated differences of squares, Endpoint 3 (8 and 10) has the smallest difference, making it the most suitable choice for using polynomial identities to convert differences of numerical squares into products. Hence, the answer is option 3.