Bài 1:
a) $f ( x ) = -3x^5 - 4x + 7x^3- 2x + 2x^5 -6 + x^2- 5 $
$=-x^5+7x^3+x^2-6x-11$
$g ( x ) = x - x^5 + x^2- 2x + x^5 - 3x^2- 4 + x^3- 10 $
$=x^3-2x^2-x-14$
b) $f(x)+g(x)=-x^5+7x^3+x^2-6x-11+(x^3-2x^2-x-14)$
$=-x^5+7x^3+x^2-6x-11+x^3-2x^2-x-14$
$=-x^5+8x^3-x^2-7x-25$
c) $f(x)+g(x)=-x^5+7x^3+x^2-6x-11-(x^3-2x^2-x-14)$
$=-x^5+7x^3+x^2-6x-11-x^3+2x^2+x+14$
$=-x^5+6x^3+3x^2-5x+3$
d) $f(x)-3g(x)=-x^5+7x^3+x^2-6x-11-3(x^3-2x^2-x-14)$
$=-x^5+7x^3+x^2-6x-11-3x^3+6x^2+3x+42$
$=-x^5+4x^3+8x^2-3x+31$
Bài 2:
a) $3x - 2=0\Leftrightarrow x=\dfrac23$
b) $\dfrac{-5x}3 - 7=0\Leftrightarrow \dfrac{-5x}3 =7$
$\Leftrightarrow x=\dfrac{-21}{5}$
c) $( x - 3 ) . ( x - 4 )=0$
$\Leftrightarrow \left[\begin{array}{I}x=3\\x=4\end{array}\right.$
d) $x ² - 2x=0$
$\Leftrightarrow x(x-2)=0$
$\Leftrightarrow \left[\begin{array}{I}x=0\\x=2\end{array}\right.$
e) $x ³ - 4x$
$\Leftrightarrow x(x^2-4)=0$
$\Leftrightarrow x(x-2)(x+2)$
$\Leftrightarrow \left[\begin{array}{I}x=0\\x=\pm2\end{array}\right.$
f) $x ² + 2=0$
Do $x^2\ge0$
$\Rightarrow x^2+2\ge2$
$\Rightarrow x^2+2\ne 0$
Vậy nên đa thức không có nghiệm.
g) $x ² - 5x + 4=0$
$\Leftrightarrow x^2-4x-x+4$
$\Leftrightarrow x(x-4)-(x-4)=0$
$\Leftrightarrow (x-4)(x-1)=0$
$\Leftrightarrow \left[\begin{array}{I}x=1\\x=4\end{array}\right.$
h) $x ² + 4x + 5 =0$
Ta có: $x^2+4x+5=x^2+4x+4+1=(x+2)^2+1$
Do $(x+2)^2\ge0$
$\Rightarrow (x+2)^2+1\ge1$
$\Rightarrow (x+2)^2+1\ne0$ nên đa thức không có nghiệm.