Final answer:
To factor the perfect square x²+10x+25, we identify it as (x+5)² by recognizing that the first and last terms are squares of x and 5 respectively, and the middle term is twice the product of x and 5.
Step-by-step explanation:
To factor the given perfect square x²+10x+25, we look for a binomial (ax+b) such that (ax+b)² = x²+10x+25. Since the last term in the trinomial is a square of 5 (because 5² = 25), and the middle term is twice the product of x and 5 (since 2 * x * 5 = 10x), we can conclude that the binomial is (x+5). Hence, (x+5)² = x²+10x+25. This factoring is quicker and more straightforward than using the quadratic formula and is a standard approach for perfect square trinomials.