Final answer:
The area of a rectangular painting given by the trinomial x^2 + x - 42 can be factored to (x + 7)(x - 6), which represent its possible dimensions.
Step-by-step explanation:
The area of a rectangular painting is given by the trinomial x2 + x - 42. To find the possible dimensions of the painting, we need to factor this expression. Factoring quadratics is a method to express the quadratic in the form of (x + m)(x + n) where m and n are numbers that, when multiplied, give the constant term (-42), and when added, give the coefficient of the linear term. Looking for two numbers that multiply to -42 and add to 1, we find 7 and -6. Thus, the trinomial can be factored as (x + 7)(x - 6). These factors represent the possible dimensions of the rectangular painting. So, the dimensions of the painting could be x + 7 and x - 6.