# Factor each polynomial. 12t^{4}-t^{2}-35

Factor each polynomial.
$12{t}^{4}-{t}^{2}-35$
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Ethan Sanders
Step 1
To Factor polynomial.
$P\left(x\right)=12{t}^{4}-{t}^{2}-35$
Take $u={t}^{2}$
$P\left(x\right)=12{u}^{2}-u-35$
$u=\frac{-b\sqrt{{b}^{2}-4ac}}{2a}$
Step 2
$P\left(x\right)=12{u}^{2}-u-35$
$u=\frac{-1±\sqrt{{\left(-1\right)}^{2}-4\left(12\right)\left(-35\right)}}{2\left(-1\right)}$
$u=\frac{-1±\sqrt{1+1680}}{-2}$
$u=\frac{-1±\sqrt{1681}}{-2}$
$u=\frac{-1±41}{-2}$
$u=\frac{-1+41}{-2}$ and $u=\frac{-1-41}{-2}$
u=-20 and u=21
Plug in $u={t}^{2}$
${t}^{2}=-20$ and ${t}^{2}=21$
${t}^{2}=-20$ is not possible
Therefore,
${t}^{2}=21$
$t=±\sqrt{21}$

Melinda McCombs
Step 1
Given polynomial is, $12{t}^{4}-{t}^{2}-35$.
It is factorize as follows:
$12{t}^{4}-{t}^{2}-35$.
Let $u={t}^{2}$.
$12{t}^{4}-{t}^{2}-35=12{u}^{2}-u-35$
Step 2
Further simplification,
$12{u}^{2}-u-35=\left(3u+5\right)\left(4u-7\right)$
$=\left(3{t}^{2}+5\right)\left(4{t}^{2}-7\right)$