Factor the expression c^4+11c^2+28

 Exercise

$c^4+11c^2+28$

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We can factor the fourth degree trinomial $c^4+11c^2+28$ by applying the substitution: $y=c^2$

$y^2+11y+28$

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Factor the trinomial $y^2+11y+28$ finding two numbers that multiply to form $28$ and added form $11$

$\begin{matrix}\left(4\right)\left(7\right)=28\\ \left(4\right)+\left(7\right)=11\end{matrix}$

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

$\left(y+4\right)\left(y+7\right)$

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Replace $y$ with the original variable

$\left(c^2+4\right)\left(c^2+7\right)$

$\left(c^2+4\right)\left(c^2+7\right)$

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