Question

Factorise x cube - 3x square - 9x - 5

Answer 1

 p(x) = x3 - 3x2 - 9x - 5

Factors of 5 = 1,5,-1,-5

p(1) = 13 - 3 x (1)2  - 9 x (1) - 5

       = 1 -3 - 9 - 5 

       = 1 - 17 = - 16 ≠ 0

p(-1) = (-1)3 x 3 x (-1)2 - 9 x (-1) -5

        = -1 - 3 + 9 - 5 = -9 + 9 = 0

p(-1) =0

∴ (x+1) is a factor of p(x)

    p(x) ÷ (x+1)

    x3 - 3x2 - 9x - 5 ÷ x + 1

    = x2 - 4x - 5

x2 - 4x - 5

x2 - 5x + 1x - 5 

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

= ( x - 5) ( x + 1)

Answer 2

Step-by-step explanation:

Given :

A polynomial x^3 - 3x^2 - 9x - 5

To Find :

Three factors of polynomial x^3 - 3x^2 - 9x - 5

Solution :

Constant Term = -5

Factors of Constant Term = 1,5

Putting x = 1 :

→ (1)^3 - 3(1)^2 - 9(1) - 5

→ 1 - 3 - 9 - 5

→ 1 - 17

→ - 16

Putting x = -1 :

→ (-1)^3 - 3(-1)^2 -9(-1) - 5

→ - 1 - 3 + 9 - 5

→- 4 + 9 - 5

→5 - 5

→ 0

• x = -1 is the root .

• x + 1 is the factor.

(Refer to the attachment)

Now :

→ x^2 - 4x - 5

→ x^2 - (5x - 1x) - 5

→ x^2 - 5x + 1x - 5

→x(x - 5) + 1(x - 5)

→ (x + 1)(x - 5)

So , The three factors are (x+1) , (x-5) , (x+1)...