Question

Factorise: x cube minus 3 x square - 3 x minus 5​

Answer 1

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▪️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

Answer:

(x-5) (x+1) is the answer