Question

Factorise x³-3x²-9x-5​

Answer 1

x³ - 3x² - 9x - 5

= x³ + x² - 4x² - 4x  - 5x - 5

= x²(x+1) - 4x(x+1) -5(x+1)

= (x+1)(x² - 4x - 5)

= (x+1)(x² - 5x + x - 5)

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

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

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

=(x+1)²(x-5)

Answer 2

${\huge{\underline{\underline{\bold{\red{Answer:-}}}}}}$

$x^3 - 3x^2 - 9x - 5=(x+1)^2(x-5)$

Step-by-step explanation:

$x^3 - 3x^2 - 9x - 5$

$⇒$ $x^3+ x^2 - 4x^2 - 4x - 5x - 5$

$⇒$$x^2(x+1) - 4x(x+1) -5(x+1)$

$⇒$$(x+1)(x^2 - 4x - 5)$

$⇒$$(x+1)(x^2- 5x + x - 5)$

$⇒$$(x+1)[x(x-5) + 1(x-5)]$

$⇒$ $(x+1)[(x-5)(x+1)]$

$⇒$$(x+1)(x+1)(x-5)$

$⇒$$(x+1)^2(x-5)$

$Hence$

$x^3 - 3x^2 - 9x - 5=(x+1)^2(x-5)$