Question

factorise the following polynomial (x2-6x)2-8(x2-6x+8)-64​

Answer 1

Answer:

(x^2-6x )^2 - 8 ( x^2 -6x +8) -64

put x^2 -6x = m

m^2 - 8 (m +8) - 64

m^2 - 8 m - 64 - 64

m^2 - 8 m - 128

m ^ 2 - 16 m + 8 m - 128

m (m - 16 ) + 8 ( m - 16)

(m - 16) (m +8)

resubstitute the value of m

(x^2 - 6x -16) ( x^2 - 6x +8)

(x^2 -8 x +2x -16) (x^2-4x -2x +8)

[ x (x -8) +2 (x-8)] [ x (x -4) -2 (x -4)]

(x-8) (x+2) (x-4) (x-2)

Answer 2

Answer:

(x^2-6x )^2 - 8 ( x^2 -6x +8) -64

put x^2 -6x = m

m^2 - 8 (m +8) - 64

m^2 - 8 m - 64 - 64

m^2 - 8 m - 128

m ^ 2 - 16 m + 8 m - 128

m (m - 16 ) + 8 ( m - 16)

(m - 16) (m +8)

resubstitute the value of m

(x^2 - 6x -16) ( x^2 - 6x +8)

(x^2 -8 x +2x -16) (x^2-4x -2x +8)

[ x (x -8) +2 (x-8)] [ x (x -4) -2 (x -4)]

(x-8) (x+2) (x-4) (x-2)

Step-by-step explanation:

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