Question

factorise it with splitting method

x^4 - 3x^ 2 + 2​

Answer 1

$x^4 - 3x^ 2 + 2 \\ = > {x}^{4} - 2 {x}^{2} - {x}^{2} + 2 \\ = > {x}^{2} ( {x}^{2} - 2) - 1( {x}^{2} - 2) \\ = > ( {x}^{2} - 2)( {x}^{2} - 1)$

Answer 2

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Very easy, put x=1 , the polynomial will evaluate to 0 . This means that (x−1) is a factor of the polynomial.

x4–3x2+2

=x4−x3+x3−x2–2x2+2

=x3(x−1)+x2(x−1)−2(x2–1)

=x3(x−1)+x2(x−1)−2(x+1)(x−1)

=(x−1){x3+x2–2(x+1)}

=(x−1)(x3+x2–2x−2)

=(x−1){x2(x+1)−2(x+1)}

=(x−1)(x+1)(x2−2)