a: Đặt 3-x=0

=>x=3

Đặt x+2=0

=>x=-2

Bảng xét dấu:

f(x)>0 khi -2<x<3

f(x)=0 khi x∈{-2;3}

f(x)<0 khi x<-2 hoặc x>3

b: \(f\left(x\right)=\left(x-1\right)\left(x^2-6x-7\right)\)

\(=\left(x-1\right)\left(x-7\right)\left(x+1\right)\)

Đặt x-1=0

=>x=1

Đặt x-7=0

=>x=7

Đặt x+1=0

=>x=-1

Bảng xét dấu:

f(x)>0 khi -1<x<1 hoặc x>7

f(x)=0 khi x∈{-1;1;7}

f(x)<0 khi x<-1 hoặc 1<x<7

c:

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

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

=-3x(x-1)-2(x-1)

=(x-1)(-3x-2)

Đặt f(x)=0

=>(x-1)(-3x-2)=0

=>\(\left[\begin{array}{l}x=-\frac23\\ x=1\end{array}\right.\)

Bảng xét dấu:

f(x)>0 khi -2/3<x<1

f(x)=0 khi x∈{-2/3;1}

f(x)<0 khi x<-2/3 hoặc x>1

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

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

Đặt f(x)=0

=>(2x-1)(x-1)\(\left(x^2+x+1\right)=0\)

=>(2x-1)(x-1)=0

=>x=1/2 hoặc x=1

Bảng xét dấu:

f(x)>0 khi x<1/2 hoặc x>1

f(x)=0 khi x=1/2 hoặc x=1

f(x)<0 khi 1/2<x<1

\(f\left(x;y\right)=3x^2+y^2-2x-xy+y+3\)

\(=\left(x^2-xy+\dfrac{y^2}{4}\right)+\dfrac{1}{2}\left(4x^2-4x+1\right)+\dfrac{1}{3}\left(\dfrac{9}{4}y^2+3y+1\right)+\dfrac{13}{6}\)

\(=\left(x-\dfrac{y}{2}\right)^2+\dfrac{1}{2}\left(2x-1\right)^2+\dfrac{1}{3}\left(\dfrac{3y}{4}+1\right)^2+\dfrac{13}{6}>0;\forall x;y\)