Final answer:
The expression 8-50x^2 cannot be factored into trinomials. Instead, by recognizing it as a difference of squares, it can be factored as (5x - 2)(5x + 2), which yields a binomial factorization.
Step-by-step explanation:
The expression 8-50x^2 is given to us, and we are asked to factor it into trinomials. However, factoring this expression would typically result in factoring a difference of squares if it can be factored over the integers. Since there are no trinomial forms that can be derived from 8-50x^2, let us explore the factoring of the difference of squares.
The expression can be rewritten as 25x^2 - (2²), so factored form would be (5x - 2)(5x + 2). This is the factored form of the given binomial, not a trinomial, because it is a difference of squares.
The expression 8-50x^2 can be factored into trinomials as follows:
First, factor out the greatest common factor, which is 2. So, 8-50x^2 becomes 2(4-25x^2).
Next, recognize that 4-25x^2 is a difference of squares. So, use the formula (a^2 - b^2) = (a + b)(a - b) to factor it further. In this case, a = 2 and b = 5x. So, 4-25x^2 factors into (2 + 5x)(2 - 5x).
Therefore, the expression 8-50x^2 can be factored into trinomials as 2(2 + 5x)(2 - 5x).