Question

Factorise: i) x^3-3x^2-9x-5. ii) 2y^3+y^2-2y-1

Answer 1

(i) x³ - 3x² - 9x - 5

= x³ - 5x² + 2x² - 10x + x - 5

= x²(x - 5) + 2x(x - 5) + 1(x - 5)

= (x - 5)(x² + 2x + 1)

= (x - 5)(x² + x + x + 1)

= (x - 5)[x(x + 1) + 1(x + 1)]

= (x - 5)(x + 1)(x + 1).

(ii) 2y³ + y² - 2y - 1

= y²(2y + 1) - 1(2y + 1)

= (y² - 1)(2y + 1)

= [(y)² - (1)²](2y + 1)

= (y - 1)(y + 1)(2y + 1).