Question

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

Answer 1

x³ - 5x² + 8x - 6

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)

Answer 2

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