Factorize: x3–23x2+ 142 x -120

Step-by-step explanation:

x³ - 23x² + 142x - 120

x³ - x² - 22x² + 22x + 120x - 120

x²(x - 1) - 22x(x - 1) + 120(x - 1)

(x - 1)(x² - 22x + 120)

(x - 1)(x² - 10x - 12x + 120)

(x - 1)[x(x - 10) - 12(x - 10)]

(x - 1) (x - 10) (x - 12)

468

step-by-step explanation:

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.