Factor the expression x^4-x^2+1

 Exercise

$x^4-x^2+1$

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We can factor the fourth degree trinomial $x^4-x^2+1$ by applying the substitution: $y=x^2$

$y^2-y+1$

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Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$y^2-y+1+\frac{1}{4}-\frac{1}{4}$

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Factor the perfect square trinomial $y^2+-1+\frac{1}{4}$

$\left(y- \frac{1}{2}\right)^2+1-\frac{1}{4}$

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Simplify the addition $\left(y- \frac{1}{2}\right)^2+1-\frac{1}{4}$

$\left(y- \frac{1}{2}\right)^2+\frac{3}{4}$

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Multiply the fraction and term in $- \frac{1}{2}$

$\left(y-\frac{1}{2}\right)^2+\frac{3}{4}$

$\left(y-\frac{1}{2}\right)^2+\frac{3}{4}$

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