What is the HCF of \(x^3 + x^2y - 10xy^2 + 8y^3\) and \(x^3 + x^2y - 4xy^2 - 4y^3\)?
\((x-2y)\)
Factorise both polynomials completely: \(x^3+x^2y-10xy^2+8y^3=(x-y)(x-2y)(x+4y)\).
\(x^3+x^2y-4xy^2-4y^3=(x-2y)(x+y)(x+2y)\).
The only common factor of the two polynomials is \((x-2y)\), so the HCF is \((x-2y)\).
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