Đáp án:
\(\begin{array}{l}
a)A = \left( {x - 5} \right)\left( {x + 2} \right)\\
b)B = \left( {3x + 1} \right)\left( {2x - 3} \right)\\
c)C = \left( {2\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)\\
d)D = \left( {{x^2} + x + 1} \right)\left( {x + 3} \right)\\
e)E = \left( {2\sqrt x + 1} \right)\left( {x + \sqrt x + 3} \right)
\end{array}\)
Giải thích các bước giải:
\(\begin{array}{l}
a)A = {x^2} - 3x - 10\\
= {x^3} - 5x + 2x - 10\\
= x\left( {x - 5} \right) + 2\left( {x - 5} \right)\\
= \left( {x - 5} \right)\left( {x + 2} \right)\\
b)B = 6{x^2} - 7x - 3\\
= 6{x^2} + 2x - 9x - 3\\
= 2x\left( {3x + 1} \right) - 3\left( {3x + 1} \right)\\
= \left( {3x + 1} \right)\left( {2x - 3} \right)\\
c)C = 2x - \sqrt x - 3\\
= 2x - 3\sqrt x + 2\sqrt x - 3\\
= \sqrt x \left( {2\sqrt x - 3} \right) + \left( {2\sqrt x - 3} \right)\\
= \left( {2\sqrt x - 3} \right)\left( {\sqrt x + 1} \right)\\
d)D = {x^3} + 4{x^2} + 4x + 3\\
= {x^3} + 3{x^2} + {x^2} + 3x + x + 3\\
= {x^2}\left( {x + 3} \right) + x\left( {x + 3} \right) + \left( {x + 3} \right)\\
= \left( {{x^2} + x + 1} \right)\left( {x + 3} \right)\\
e)E = 2x\sqrt x + 3x + 7\sqrt x + 3\\
= 2x\sqrt x + x + 2x + \sqrt x + 6\sqrt x + 3\\
= x\left( {2\sqrt x + 1} \right) + \sqrt x \left( {2\sqrt x + 1} \right) + 3\left( {2\sqrt x + 1} \right)\\
= \left( {2\sqrt x + 1} \right)\left( {x + \sqrt x + 3} \right)
\end{array}\)
