Giải thích các bước giải:
$\begin{array}{l}
b)6{a^4} + 7{a^3} - 37{a^2} - 8a + 12\\
= 6{a^4} - 12{a^3} + 19{a^3} - 38{a^2} + {a^2} - 2a - 6a + 12\\
= \left( {a - 2} \right)\left( {6{a^3} + 19{a^2} + a - 6} \right)\\
= \left( {a - 2} \right)\left( {6{a^3} + 18{a^2} + {a^2} + 3a - 2a - 6} \right)\\
= \left( {a - 2} \right)\left( {a + 3} \right)\left( {6{a^2} + a - 2} \right)\\
= \left( {a - 2} \right)\left( {a + 3} \right)\left( {6{a^2} + 4a - 3a - 2} \right)\\
= \left( {a - 2} \right)\left( {a + 3} \right)\left( {3a + 2} \right)\left( {2a - 1} \right)\\
d)\left( {{x^2} + 3x - 4} \right)\left( {{x^2} + x - 6} \right) - 24\\
= \left( {x - 1} \right)\left( {x + 4} \right)\left( {x - 2} \right)\left( {x + 3} \right) - 24\\
= \left( {x - 1} \right)\left( {x + 3} \right)\left( {x - 2} \right)\left( {x + 4} \right) - 24\\
= \left( {{x^2} + 2x - 3} \right)\left( {{x^2} + 2x - 8} \right) - 24\\
= {\left( {{x^2} + 2x} \right)^2} - 11\left( {{x^2} + 2x} \right) + 24 - 24\\
= {\left( {{x^2} + 2x} \right)^2} - 11\left( {{x^2} + 2x} \right)\\
= \left( {{x^2} + 2x} \right)\left( {{x^2} + 2x - 11} \right)\\
= x\left( {x + 2} \right)\left( {{x^2} + 2x - 11} \right)\\
f)\left( {x - 4} \right)\left( {x - 5} \right)\left( {x - 6} \right)\left( {x - 7} \right) - 1680\\
= \left( {x - 4} \right)\left( {x - 7} \right)\left( {x - 5} \right)\left( {x - 6} \right) - 1680\\
= \left( {{x^2} - 11x + 28} \right)\left( {{x^2} - 11x + 30} \right) - 1680\\
= {\left( {{x^2} - 11x} \right)^2} + 58\left( {{x^2} - 11x} \right) + 28.30 - 1680\\
= {\left( {{x^2} - 11x} \right)^2} + 58\left( {{x^2} - 11x} \right) - 840\\
= {\left( {{x^2} - 11x} \right)^2} + 70\left( {{x^2} - 11x} \right) - 12\left( {{x^2} - 11x} \right) - 840\\
= \left( {{x^2} - 11x + 70} \right)\left( {{x^2} - 11x - 12} \right)\\
= \left( {{x^2} - 11x + 70} \right)\left( {x + 1} \right)\left( {x - 12} \right)
\end{array}$
