Write the polynomial as the product of factors that are irreducible over the rat

Reggie

Reggie

Answered question

2021-09-22

Write the polynomial as the product of factors that are irreducible over the rationals, f(x)=x4+6x227

Answer & Explanation

Aniqa O'Neill

Aniqa O'Neill

Skilled2021-09-23Added 100 answers

Let us factor the given polynomial function as the product of factors that are irreducible over the rationals
f(x)=x4+6x227
=x4+9x23x227
=(x4+9x2)(3x2+27)
Let us factor out x2 and -3:
=x2(x2+9)3(x2+9)
=(x23)(x2+9)
Result: (x23)(x2+9)

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