Given that f (x) = x^3 + 2x^2 + 1, g (x) = - x^3 - x^2 - 4x + 4, h (x) = f (x) + g (x), and h (x) = 1, what is the value of x?

x = 2

Step-by-step explanation:

h (x) = f (x) + g (x) = x³ + 2x² + 1 - x³ - x² - 4x + 4 ← collect like terms, thus

h (x) = f (x) + g (x) = x² - 4x + 5

Given

h (x) = 1, then

x² - 4x + 5 = 1 (subtract 1 from both sides)

x² - 4x + 4 = 0 ← in standard form

(x - 2) ² = 0 ← in factored form (perfect square), thus

x - 2 = 0 ⇒ x = 2