2017 · Q19
The factors of x (x + 2) (x + 3) (x + 5) - 72 are
Elementary MathematicsAlgebra
- Ax, (x + 3), (x + 4) and (x - 6)
- B(x - 1), (x + 6) and (x² - 2x - 12)
- C(x - 1), (x + 6) and (x² + 5x + 12)
- D(x + 1), (x - 6) and (x² - 5x - 12)
Explanation
Group the factors: x(x+5) = x²+5x and (x+2)(x+3) = x²+5x+6. Setting t = x²+5x, the expression becomes t(t+6)−72 = t²+6t−72 = (t+12)(t−6). Back-substituting: (x²+5x+12)(x²+5x−6) = (x²+5x+12)(x−1)(x+6). Hence option (C).