How do you determine if a polynomial is the difference of two squares?
To determine if a polynomial is the difference of two squares, follow these steps:
1. Identify the polynomial: Write down the given polynomial in its standard form. For example, let's consider the polynomial 16x^2 - 9.
2. Factor the polynomial: Factor the given polynomial as much as possible. For the example polynomial, we have 16x^2 - 9 = (4x)^2 - 3^2.
3. Determine if it is the difference of two squares: Look at the factored form of the polynomial. If it can be written as the difference of two perfect squares, then the polynomial itself is the difference of two squares. In the example, we have (4x)^2 - 3^2, which can be written as (4x - 3)(4x + 3).
4. Verify the result: Multiply the two factors obtained from the factored form. If the product equals the original polynomial, then it is confirmed that the polynomial is the difference of two squares. In our example, (4x - 3)(4x + 3) = 16x^2 - 9, thus confirming that the original polynomial is the difference of two squares.
In summary, to determine if a polynomial is the difference of two squares, factor the polynomial and see if it can be written as the difference of two perfect squares.