Question

How many factors are there for the expression x − x 17 ?

Answer 1

x (1 + x8) (1 + x4) (1 + x2)(1 + x)(1 – x)

By using (a2 -b2) = (a + b)(a - b), we can get factors:

x – x 17

= x (1 – x16)

= x {(1)2 – (x8)2}

= x {(1 + x8)( 1 - x8)}

= x (1 + x8){(1)2 – (x4)2}

= x (1 + x8) (1 + x4) (1 – x4)

= x (1 + x8) (1 + x4) {(1)2 – (x2)2}

= x (1 + x8) (1 + x4) (1 + x2) (1 – x2)

= x (1 + x8) (1 + x4) (1 + x2) {(1)2 – (x)2}

= x (1 + x8) (1 + x4) (1 + x2)(1 + x)(1 – x)


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