Factor the expression x^4+4x^2+3

 Exercise

$x^4+4x^2+3$

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We can factor the fourth degree trinomial $x^4+4x^2+3$ by applying the substitution: $y=x^2$

$y^2+4y+3$

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Factor the trinomial $y^2+4y+3$ finding two numbers that multiply to form $3$ and added form $4$

$\begin{matrix}\left(1\right)\left(3\right)=3\\ \left(1\right)+\left(3\right)=4\end{matrix}$

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Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values

$\left(y+1\right)\left(y+3\right)$

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Replace $y$ with the original variable

$\left(x^2+1\right)\left(x^2+3\right)$

$\left(x^2+1\right)\left(x^2+3\right)$

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