Question

FACTORISE

${x}^{3} - 3 {x}^{2} - 9x - 5$
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Answer 1

Answer:

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)