Factor. x 5 + x + 1

termegolz6

termegolz6

Answered

2022-07-14

Factor. x 5 + x + 1

Answer & Explanation

Danica Ray

Danica Ray

Expert

2022-07-15Added 15 answers

We can add and subtract + x 2 x 2 = 0 without changing the expression:
x 5 + x + 1 = ( x 5 x 2 ) + ( x 2 + x + 1 ) = x 2 ( x 3 1 ) + ( x 2 + x + 1 ) = x 2 ( x 1 ) ( x 2 + x + 1 ) + ( x 2 + x + 1 )
Now factor out the common factor...which gives us
( x 2 ( x 1 ) + 1 ) ( x 2 + x + 1 ) = ( x 3 x 2 + 1 ) ( x 2 + x + 1 )

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