(*Video 1: Factoring some polynomials*)

Factor[x^2-4x+4]

Expand[(((-3+x))^2)]
Expand[(((x-3))^2)]

Factor[x^2-2c x+c^2]

Expand[(((a-x))^2)]

Factor[x^2-1/3 x+1/36]

Solve[-2c==-1/3,c]

Simplify[(1/36) (((-1+6 x))^2)==((((1/6)-x))^2)]

Factor[x^2-16]

Factor[(x^4)-10 (x^2)+25]

Expand[(x-2)^3]

Factor[-8+12 x-6 (x^2)+(x^3)]

Expand[(x-2)^15]

Factor[-32768+245760 x-860160 (x^2)+1863680 (x^3)-2795520 (x^4)+3075072 (x^5)-2562560 (x^6)+1647360 (x^7)-823680 (x^8)+320320 (x^9)-96096 (x^10)+21840 (x^11)-3640 (x^12)+420 (x^13)-30 (x^14)+(x^15)]

(*Video 2: Plots *)

Plot[x^2-6x+9,{x,0,6}]

Factor[x^2-6x+9](* (x-3)^2 *)

Plot[(((-5+x))^2),{x,4,6}]

Manipulate[Plot[t(x-a)^2+c,{x,-10,10},PlotRange->{-2,2}],{a,-10,10},{c,-2,2},{t,-2,2}]

Plot[x^2-6x+9,{x,-3,7},AspectRatio->1]

Plot[(x^2-6x+9)/(x-3),{x,-2,5}]

Simplify[(x^2-6x+9)/(x-3)]

Plot[(x^2-6x+9)/(x-5),{x,-4,10}]

(*Video 3: Limits *)

Limit[x^2-6x+9,x->1]

x=1;
x^2-6x+9

Plot[{x^2-6x+9,4},{x,0,4}]

Limit[(x^2-6x+9)/(x-2),x->1]

Plot[{(x^2-6x+9)/(x-2),-4},{x,0,1.5},PlotRange->{-5,-3}]

(*There IS a single value (yellow line) where the function accumulates!*)

Limit[(x^2-6x+9)/(x-2),x->2]

(*Recall the plot:*)
Plot[{(x^2-6x+9)/(x-2),Table[{n},{n,-100,100,10}]},{x,1.7,2.3},PlotRange->100]

(*There is no single value (yellow line) where the function accumulates!*)

(*Directional limit*)
Limit[(x^2-6x+9)/(x-2),x->2,Direction->"FromBelow"]

(*Directional limit*)
Limit[(x^2-6x+9)/(x-2),x->2,Direction->"FromAbove"]

(*Directional limit*)
Limit[(x^2-6x+9)/(x-2),x->2,Direction->"FromBelow"]
Limit[(x^2-6x+9)/(x-2),x->2,Direction->"FromAbove"]

Limit[(x^2-6x+9)/(x-2),x->2]