MASTERSHEET 
Copy/Paste Formulae for Chapter 6 Polynomials

>Copy the formula you need
>Paste it into the other workbook you are using
>NOTE: Do NOT alter the formulae in this workbook, these are your templates only.

Handy Shortcuts

Shift+Enter to execute a command
Ctrl-s save your file
Alt+7 to start a text cell
Ctrl-/ gives a fraction (□/□)
Ctrl-2 gives a square root sign (Sqrt[□])
Ctrl-6 gives an exponent (□^□)

All Mathematica commands start with a Capital and use square brackets [ ]
For examples Plot [ ]

MATHEMATICA COMMANDS FOR Chapter 6

1. Binomial Expand

Expand["Enter Expression here"]//TraditionalForm

Expand[(x+10)(x-9)]//TraditionalForm

Expand[(x+1)(x-2)(x-3)]//TraditionalForm

2. Factorise Expressions

Factor["Enter Expression here"]//TraditionalForm

Factor[5*(a+b)+v*(a+b)]//TraditionalForm

Factor[1/4-3d+9d^2]//TraditionalForm

Factor[45t^2-20]//TraditionalForm

3. Solve Equations

a.  Solve Equations

Solve["Enter Equation here with ==","the thing you are looking for"]//N

b.  Solve Equations

Roots["Enter Equation here with ==","the thing you are looking for"]//N

Solve[(3x-17)(2x-d)==0,x]//N

4. Graph Equations

ContourPlot[{y=="Enter Polynomial here"},{x,"Minimum","Maximum"},{y,"Minimum","Maximum"},PlotLegends->"Expressions"]

ContourPlot[{y==(x-2)^4+5},{x,0,10},{y,0,10},PlotLegends->"Expressions"]

TableForm[Table[{"Enter Equation here"},{x,"Minimum value for x","Maximum value for x"}]]

TableForm[Table[{y=x^2},{x,-3,3}]]//N

5. Highest Common Factor( HCF), Lowest Common Multiple(LCM)

LCM["Enter all numbers with a comma in between"]

GCD["Enter all numbers with a comma in between"]

LCM[2,3,5]

GCD[2, 3, 5]

6. Solve Quadratic Equations by using discriminant

discriminant[a_,b_,c_]:=(b^2)-4*a*c
lm=discriminant["a","b","c"]//N
Print["Discriminant = ",Normal[lm]]
solution1[a_,b_,c_]:=((-b+(Sqrt[(b^2)-4*a*c]))/(2*a))
lm=solution1["a","b","c"]//N
Print["Solution1 = ",Normal[lm]]
solution2[a_,b_,c_]:=((-b-(Sqrt[(b^2)-4*a*c]))/(2*a))
lm=solution2["a","b","c"]//N
Print["Solution2 = ",Normal[lm]]

discriminant[a_,b_,c_]:=(b^2)-4*a*c
lm=discriminant[1,7,-3]//N
Print["Discriminant = ",Normal[lm]]
solution1[a_,b_,c_]:=((-b+(Sqrt[(b^2)-4*a*c]))/(2*a))
lm=solution1[1,7,-3]//N
Print["Solution1 = ",Normal[lm]]
solution2[a_,b_,c_]:=((-b-(Sqrt[(b^2)-4*a*c]))/(2*a))
lm=solution2[1,7,-3]//N
Print["Solution2 = ",Normal[lm]]

7. Substitution: Defining a polynomial as a function and find a value

p1[x_]:="Enter Polynomial here"//TraditionalForm
p1[x]

p1[x_]:=(x^4)-3(x^3)+2(x^2)-1//TraditionalForm
p1[x]

p1[1]

p2[x_]:=2(x^4)-(x^3)+2c x+6//TraditionalForm
p2[x]

Solve[p2[1]==21,c]

8. Finding values of a  polynomial in a table

Table["Enter Polynomial here",{x,"Minimum value for x","Maximum value for x"}]

Table[(x^3)-3(x^2)-2x+1,{x,-2,2}]

9.  Polynomial long division with quotient and remainder

PolynomialQuotientRemainder["Enter Polynomial here","Enter Quotient here","Enter Variable (x) here"]//TraditionalForm

PolynomialQuotientRemainder[(x^3)+3(x^2)+2x+1,x-2,x]//TraditionalForm

10. Graphs of polynomials with Maximum Minimum and X-intercepts

ContourPlot[{y=="Enter Polynomial here"},{x,"Minimum","Maximum"},{y,"Minimum","Maximum"},PlotLegends->"Expressions"]
lm=FindMaximum["Enter Polynomial here",x]
Print["Maximum->",Normal[lm]]
lm=FindMinimum["Enter Polynomial here",x]
Print["Minimum->",Normal[lm]]
lm=Roots["Enter Polynomial here"==0,x]
Print["Roots/x-Intercepts -> ",Normal[lm]]

ContourPlot[{y==16-x^4},{x,-5,5},{y,-20,20}]
lm=FindMaximum[16-x^4,x]
Print["Maximum->",Normal[lm]]
lm=FindMinimum[16-x^4,x]
Print["Minimum->",Normal[lm]]
lm=Roots[16-x^4==0,x]
Print["Roots/x-Intercepts -> ",Normal[lm]]

11. Find x-intercepts,  y-intercepts of a Function

lm=Solve[y=="Right side of Equation",y]/.x->0
Print["Y-intercepts  ",Normal[lm]]
lm=Roots[0=="Right side of Equation",x]
Print["Roots/ X-intercepts",Normal[lm]]

lm=Solve[y==(x-2)(x-2)(x^2+1),y]/.x->0
Print["Y-intercepts",Normal[lm]]
lm=Roots[0==(x-2)(x-2)(x^2+1),x]
Print["Roots/X-intercepts  ",Normal[lm]]

12. Expansion of (((a+b))^n)

Table[Expand[(((a+b))^n)],{n,0,5}]//TableForm

13. Complete the square

a:={"Enter the value for a here"}
b:={"Enter the value for b here"}
c:={"Enter the value for c here"}
Print["CompleteThe Square=",a(((x+(b/(2a))))^2)+(c-((b^2)/(4a)))]

a:={1}
b:={4}
c:={4}
Print["CompleteThe Square=",a(((x+(b/(2a))))^2)+(c-((b^2)/(4a)))]

14. Solve Simultaneous Equations

Solve[{equation here number one,another equation here},{variable1,variable2}]

Solve[{2x+3y==6,x-2y==4},{x,y}]//N

15. Given coordinate pairs, finding polynomial function

data={{"Dot 1 Coordinate pair"},{"Dot 2 Coordinate pair"},{"Dot 3 Coordinate pair"},{"Dot 4 Coordinate pair"}};
fit=FindFormula[data,x]//TraditionalForm

data={{0,270},{1,312},{2,230},{3,0}};
fit=FindFormula[data,x]//TraditionalForm

16. Find roots from given range

f[x_]:="Enter Polynomial here";
Plot[f[x],{x,"Lower range number","Higher range number"}]
FindRoot[f[x],{x,"Lower range number"}]

f[x_]:=-x^3-3x+6;
Plot[f[x],{x,1,2}]
FindRoot[f[x],{x,1}]

17. Manipulate Cubic graphs with constant number

Manipulate[Plot[(x^3)-3(x^2)+c,{x,-10,10},PlotRange->10],{{c,0},-10,10,1}]

18. Manipulate cubic transforming graphs

Manipulate[Show[Plot[a(((x-h))^3)+k,{x,-10,10},PlotRange->10],Graphics[Text[a(((x-h))^3)+k,{7,9}]]],{{h,0},-10,10,1},{{k,0},-10,10,1},{{a,1},-10,10,0.1}]

19. Manipulate quartic transforming graphs

20. Manipulate even or odd polynomials

Manipulate[Show[Plot[{(x^n)},{x,-2,2},PlotRange->{-2,2}],Graphics[Text[(x^n),{1,-1}]]],{n,2,20,1}]