Question

Factorise : x³-3x²-9x-5​

Answer 1

Answer :

• x³ - 3x² - 9x - 5 = (x + 1)² (x - 5)
• (x + 1) (x - 5) are the factors of polynomial

Given :

• x³ - 3x² - 9x - 5

Solution :

Method (1)

》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) (x + 1)² 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) (x + 1)²

Method (2)

》x³ - 3x² - 9x - 5

》x³ + x² - 4x² - 4x - 5x - 5

》x²(x + 1) - 4x(x + 1) - 5x(x + 1)

》(x + 1) (x² - 4x - 5)

》(x + 1) (x² - 5x + x - 5)

》(x + 1) (x - 5) (x + 1)

》(x + 1)² - (x - 5)

Hence , x³ - 3x² - 9x - 5 = (x + 1)² (x - 5)

(x + 1) (x - 5) are the factors of polynomial