\(2x^3-x^2+5x+3\)

\(=2x^3+x^2-2x^2-x+6x+3\)

\(=x^2\left(2x+1\right)-2x\left(2x+1\right)+3\left(2x+1\right)\)

\(=\left(x^2-2x+3\right)\left(2x+1\right)\)

d) \(9^{2x-184}.3^2=3^6\)

\(9^{2x-184}=3^4=9^2\)

\(2x-184=2\)

\(x=93\)(TM)

e) \(16^{5x-13}.4^2=4^6\)

\(16^{5x-13}=4^4=16^2\)

\(5x-13=2\)

\(x=3\)(TM)

f) \(100^{5x+3}.10^2=10^{10}\)

\(100^{5x+3}=10^8=100^4\)

\(5x+3=4\)

\(x=\dfrac{1}{5}\)(Loại)

\(x^3-6x^2-x+30\)

\(=x^3-3x^2-3x^2+9x-10x+30\)

\(=x^2\left(x-3\right)-3x\left(x-3\right)-10\left(x-3\right)\)

\(=\left(x^2-3x-10\right)\left(x-3\right)\)

\(=\left(x^2-5x+2x-10\right)\left(x-3\right)\)

\(=\left(x\left(x-5\right)+2\left(x-5\right)\right)\left(x-3\right)\)

\(=\left(x+2\right)\left(x-5\right)\left(x-3\right)\)

\(x^3-9x^2+6x+16\)

\(=x^3-8x^2-x^2+8x-2x+16\)

\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)

\(=\left(x^2-x-2\right)\left(x-8\right)\)

\(=\left(x^2+x-2x-2\right)\left(x-8\right)\)

\(=\left(x+1\right)\left(x-2\right)\left(x-8\right)\)

\(\left(7x-12\right)^2=2^5.5^2+200\)

\(\left(7x-12\right)^2=25.32+200\)

\(\left(7x-12\right)^2=800+200\)

\(\left(7x-12\right)^2=1000=\left(10\sqrt{10}\right)^2\)

\(\Leftrightarrow\left[{}\begin{matrix}7x-12=10\sqrt{10}\\7x-12=-10\sqrt{10}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{10\sqrt{10}+12}{7}\\x=\dfrac{12-10\sqrt{10}}{7}\end{matrix}\right.\)

\(\dfrac{1}{2a}+\dfrac{2}{3b}\)

\(=\dfrac{3b+2.2a}{2a.3b}\)

\(=\dfrac{3b+4a}{6ab}\)

\(495a+1035b\)

\(=45.11a+45.23b\)

\(=45\left(11a+23b\right)⋮45\forall a,b\in N\)

Thầy nhầm đoạn cuối rồi thầy ơi

\(3^{x-1}+3^x+3^{x+1}=39\)

\(3^{x-1}+3^{x-1}.3+9.3^{x-1}=39\)

\(13.3^{x-1}=39\)

\(3^{x-1}=39:13=3\)

\(x-1=1\)

\(x=2\)