Final answer:
The given polynomial x^2+16x+55 is factored by finding two numbers that multiply to 55 and add up to 16, resulting in the factors (x + 5) and (x + 11).
Step-by-step explanation:
To factor the given polynomial x^2+16x+55, we need to find two numbers that multiply to get 55 (the constant term) and add to get 16 (the coefficient of the x term). After reviewing the factors of 55, which are 1 & 55 and 5 & 11, it is clear that the two numbers we are looking for are 5 and 11, since 5 + 11 equals 16. Therefore, the polynomial can be factored as:
(x + 5)(x + 11)
In this way, we have factored the quadratic polynomial into a product of two binomials.
To factor the polynomial x^2+16x+55, we need to find two numbers that multiply to give the constant term (55) and add up to give the coefficient of the linear term (16).
The numbers that satisfy these conditions are 5 and 11. Therefore, we can express the polynomial as (x+5)(x+11).