Let f (x) = x^2 - 2x + 2 and g (x) = x - 3. find f (x) times g (x)

x³ - 5x² + 8x - 6

Step-by-step explanation:

(x² - 2x + 2) (x - 3) ← product is required

Each term in the second factor is multiplied by each term in the first factor, that is

x² (x - 3) - 2x (x - 3) + 2 (x - 3) ← distribute all 3 parenthesis

= x³ - 3x² - 2x² + 6x + 2x - 6 ← collect like terms

= x³ - 5x² + 8x - 6 → (b)

g (x) ^2=x^2-6x+9=f (x) - 4x+7, f (x) = g (x) ^2-4g (x) - 5 = (g (x) - 2) ^2-9 = (g (x) + 7) * (g (x) - 11)

f (x) = x^2-2x+2=g (*) ^2+4x-7