Is the polynomial (x^4 - 2x^2 + 1) a perfect square? If yes, factorize it.

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Accepted Answer

Step:1 ：First, we rewrite the polynomial as ((x^2)^2 - 2(x^2) + 1)Step:2 ：We notice this is a perfect square trinomial of the form (a^2 - 2ab + b^2), where (a=x^2) and (b=1).Step:3 ：This trinomial can be factored as ((a - b)^2), which in this case gives ((x^2 - 1)^2)

Answer

Step: 1 ：First, we rewrite the polynomial as ((x^2)^2 - 2(x^2) + 1)Step: 2 ：We notice this is a perfect square trinomial of the form (a^2 - 2ab + b^2), where (a=x^2) and (b=1).Step: 3 ：This trinomial can be factored as ((a - b)^2), which in this case gives ((x^2 - 1)^2)

Is the polynomial \(x^4 - 2x^2 + 1\) a perfect square? If yes, factorize it.

Answer

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