Question

Pls answer this question I am new here.

Answer 1

To find -

Find the HCF of -

( x⁴ + x³ + 2x² + x + 1 ) and ( x³ - 1 )

First polynomial -

=> ( x⁴ + x³ + 2x² + x + 1 )

=> x⁴ + x³ + x² + x² + x + 1

=> x² ( x² + x + 1 ) + ( x² + x + 1 )

=> ( x² + 1 )( x² + x + 1 )

Second polynomial -

=> ( x³ - 1 )

=> ( x - 1 )( x² + x + 1 ) .

Now, HCF refers to the highest common factor among these polynomials, which is here , clearly ( x² + x + 1 ) .

This is the required answer .

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