a: P(x)=6x^3-4x^2+4x-2

Q(x)=-5x^3-10x^2+6x+11

M(x)=x^3-14x^2+10x+9

b: \(C\left(x\right)=7x^4-4x^3-6x+9+3x^4-7x^3-5x^2-9x+12\)

=10x^4-11x^3-5x^2-15x+21

x3+3x2-10x=0

=>x(3+3.2-10)=0

=>x=0

x3-5x2-14x=0

=>x(3-5.2-14)=0

=>x=0

x3+5x2-24x=0

=>x(3+5.2-24)=0

=>x=0

Câu a)

\(x^3+3x^2-10=0\Rightarrow x\left(x^2+3x-10\right)=0\Rightarrow x\left(x^2-2x+5x-10\right)=0\Rightarrow x\left(x\left(x-2\right)+5\left(x-2\right)\right)=0\Rightarrow x\left(x+5\right)\left(x-2\right)=0\)

\(\Rightarrow x=0;x=5;x=2\)

\(x^3-9x^2+26x-24\)

\(=x^3-4x^2-5x^2+20x+6x-24\)

\(=\left(x-4\right)\left(x^2-5x+6\right)\)

\(=\left(x-4\right)\left(x-2\right)\left(x-3\right)\)

a)7.2^x=56⇔2^x=8⇔2^x=2³⇔x=3

b)(2x+1)³=9.81⇔(2x+1)³=9³⇔2x+1=9⇔2x=8⇔x=4

c)x³=8²⇔x³=2⁶⇔x=2²⇔x=4

d)4.2^x-3=1⇔4.2^x=4⇔2^x=1⇔2^x=2⁰⇔x=0

e)2.3^x=162⇔3^x=81⇔3^x=3⁴⇔x=4

a) x = -1.                      b) x = 4 hoặc x = 5.

c) x = ± 2 .                  d) x = 1 hoặc x = 2.

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\\x=-1\end{matrix}\right.\)

\(\Leftrightarrow x^2\left(x-5\right)-\left(x-5\right)=0\\ \Leftrightarrow\left(x^2-1\right)\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-1\\x=1\\x=5\end{matrix}\right.\)

b: \(\Leftrightarrow\left(x-5\right)\left(x+1\right)\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=1\\x=-1\end{matrix}\right.\)

c: \(\Leftrightarrow\left(x-1\right)\left(x-5\right)\left(x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=5\\x=-5\end{matrix}\right.\)

a) \(5x\left(x-2000\right)-x+2000=0\)

\(\Leftrightarrow5x\left(x-2000\right)-\left(x-2000\right)=0\)

\(\Leftrightarrow\left(5x-1\right)\left(x-2000\right)=0\)

\(\Leftrightarrow x\in\left\{\frac{1}{5};2000\right\}\)

b) \(5x^2=13x\)

\(\Leftrightarrow x\left(5x-13\right)=0\)

\(\Leftrightarrow x\in\left\{0;\frac{13}{5}\right\}\)

a: 5x-20xy

\(=5x\cdot1-5x\cdot4y=5x\left(1-4y\right)\)

b: \(x^2-9=\left(x-3\right)\left(x+3\right)\)

c: \(x^2-2xy+y^2-z^2\)

\(=\left(x-y\right)^2-z^2\)

=(x-y-z)(x-y+z)

d: \(5x\left(x-1\right)-2\left(x-1\right)=\left(x-1\right)\left(5x-2\right)\)

e; \(x^2+4x+3=x^2+x+3x+3\)

=x(x+1)+3(x+1)

=(x+1)(x+3)

f: \(x^3-x+3x^2y+3xy^2+y^3-y\)

\(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left\lbrack\left(x+y\right)^2-1\right\rbrack\)

=(x+y)(x+y-1)(x+y+1)

g: \(x^2-x-y^2-y\)

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

=(x-y)(x+y)-(x+y)

=(x+y)(x-y-1)

h: \(16x-5x^2-3\)

\(=-5x^2+15x+x-3\)

=-5x(x-3)+(x-3)

=(x-3)(-5x+1)

i: \(x^3-4x=x\left(x^2-4\right)=x\left(x-2\right)\left(x+2\right)\)

j: \(2x^2-6x=2x\cdot x-2x\cdot3=2x\left(x-3\right)\)

k: \(x^3-3x^2-4x+12\)

\(=x^2\left(x-3\right)-4\left(x-3\right)\)

\(=\left(x-3\right)\left(x^2-4\right)=\left(x-3\right)\cdot\left(x-2\right)\left(x+2\right)\)

l: \(x^2-y^2-5x+5y\)

=(x-y)(x+y)-5(x-y)

=(x-y)(x+y-5)