To start, the expression x² + 9x + 18 can be factored to find its roots. We’re looking for two numbers that multiply to 18 (the constant term) and add up to 9 (the coefficient of x). In this case, the numbers 3 and 6 fit perfectly: 3 x 6 = 18 and 3 + 6 = 9.
Thus, we can write the factored form of the expression as:
(x + 3)(x + 6)
If your diagram is partially completed, it might show the initial polynomial and some indications of how the factors break it down. Each factor corresponds to a root where the expression equals zero. Here, those roots would be x = -3 and x = -6.
That’s the basic idea behind this factorization. It helps us understand the roots of the quadratic and how the polynomial can be broken down into simpler linear factors, making it easier to graph or analyze further.