Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
a,\\
{x^2} - 18x + 17 = \left( {{x^2} - x} \right) - \left( {17x - 17} \right)\\
= x.\left( {x - 1} \right) - 17\left( {x - 1} \right) = \left( {x - 1} \right).\left( {x - 17} \right)\\
b,\\
5{x^2} - 17x + 12 = \left( {5{x^2} - 5x} \right) - \left( {12x - 12} \right)\\
= 5x\left( {x - 1} \right) - 12\left( {x - 1} \right) = \left( {x - 1} \right)\left( {5x - 12} \right)\\
c,\\
{x^2} + 10x + 21 = \left( {{x^2} + 3x} \right) + \left( {7x + 21} \right)\\
= x\left( {x + 3} \right) + 7\left( {x + 3} \right) = \left( {x + 3} \right)\left( {x + 7} \right)\\
d,\\
2{x^2} - 25x + 33 = \left( {2{x^2} - 3x} \right) - \left( {22x - 33} \right)\\
= x.\left( {2x - 3} \right) - 11\left( {2x - 3} \right) = \left( {2x - 3} \right)\left( {x - 11} \right)\\
2,\\
a,\\
{2^9} - 1 = {\left( {{2^3}} \right)^3} - 1 = {8^3} - 1 = \left( {8 - 1} \right).\left( {{8^2} + 8.1 + {1^2}} \right) = 7.73\\
\Rightarrow \left( {{2^9} - 1} \right)\,\, \vdots \,\,73\\
b,\\
{5^6} - {10^4} = {5^6} - {\left( {5.2} \right)^4} = {5^6} - {5^4}{.2^4} = {5^4}.\left( {{5^2} - {2^4}} \right) = {5^4}.\left( {25 - 16} \right) = {5^4}.9\\
\Rightarrow \left( {{5^6} - {{10}^4}} \right)\,\, \vdots \,\,9
\end{array}\)
