\[\begin{array}{l}
A = 25{x^4} - 24{x^2} - 1\\
dat:{x^2} = t\left( {t \ge 0} \right)\\
= 25{t^2} - 24t - 1\\
= 25{t^2} - 25t + t - 1\\
= 25t\left( {t - 1} \right) + \left( {t - 1} \right)\\
= \left( {t - 1} \right)\left( {25t + 1} \right)\\
= \left( {{x^2} - 1} \right)\left( {25{x^2} + 1} \right)\\
= \left( {x - 1} \right)\left( {x + 1} \right)\left( {25{x^2} + 1} \right)\\
A = 64{x^4} + 63{x^2} - 1\\
dat:{x^2} = t\left( {t \ge 0} \right)\\
= 64{t^2} + 63t - 1\\
= 64{t^2} + 64t - t - 1\\
= 64t\left( {t + 1} \right) - \left( {t + 1} \right)\\
= \left( {t + 1} \right)\left( {64t - 1} \right)\\
= \left( {{x^2} + 1} \right)\left( {64{x^2} - 1} \right)\\
= \left( {{x^2} + 1} \right)\left( {8x - 1} \right)\left( {8x + 1} \right)\\
A = {x^4} - 15{x^2} + 50\\
dat:{x^2} = t\left( {t \ge 0} \right)\\
= {t^2} - 15t + 50\\
= {t^2} - 10t - 5t + 50\\
= t\left( {t - 10} \right) - 5\left( {t - 10} \right)\\
= \left( {t - 10} \right)\left( {t - 5} \right)\\
= \left( {{x^2} - 10} \right)\left( {{x^2} - 5} \right)\\
= \left( {x - \sqrt {10} } \right)\left( {x + \sqrt {10} } \right)\left( {x - \sqrt 5 } \right)\left( {x + \sqrt 5 } \right)\\
A = - 10{x^4} + 9{x^2} + 1\\
dat:{x^2} = t\left( {t \ge 0} \right)\\
= - 10{t^2} + 9t + 1\\
= - 10{t^2} + 10t - t + 1\\
= 10t\left( {1 - t} \right) + \left( {1 - t} \right)\\
= \left( {1 - t} \right)\left( {10t + 1} \right)\\
= \left( {1 - {x^2}} \right)\left( {10{x^2} + 1} \right)\\
= \left( {1 - x} \right)\left( {x + 1} \right)\left( {10{x^2} + 1} \right)\\
A = - 13{x^4} - 10{x^2} + 3\\
dat:{x^2} = t\left( {t \ge 0} \right)\\
= - 13{t^2} - 10t + 3\\
= - 13{t^2} - 13t + 3t + 3\\
= - 13t\left( {t + 1} \right) + 3\left( {t + 1} \right)\\
= \left( {t + 1} \right)\left( {3 - 13t} \right)\\
= \left( {{x^2} + 1} \right)\left( {3 - 13{x^2}} \right)\\
A = - {x^4} - 5{x^2} + 150\\
dat:{x^2} = t\left( {t \ge 0} \right)\\
= - {t^2} - 5t + 150\\
= - {t^2} + 10t - 15t + 150\\
= t\left( {10 - t} \right) + 15\left( {10 - t} \right)\\
= \left( {10 - t} \right)\left( {t + 15} \right)\\
= \left( {10 - {x^2}} \right)\left( {{x^2} + 15} \right)\\
= \left( {\sqrt {10} - x} \right)\left( {\sqrt {10} + x} \right)\left( {{x^2} + 15} \right)
\end{array}\]