x + 1

1 + x

2x^2 - x + 1

1 - x + 2 x^2

x^3 + 2x - 1

-1 + 2 x + x^3

f[x_] = 2x^2 - 1x + 1

1 - x + 2 x^2

f[x]

1 - x + 2 x^2

f[0]

1

f[25]

1226

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

-3 - x + 2 x^2

Factor[x^2 - 3x - 4]

(-4 + x) (1 + x)

Factor[f[x]]

1 - x + 2 x^2

FactorInteger[24]

{{2, 3}, {3, 1}}

FactorInteger[123456789105]

{{3, 1}, {5, 1}, {13, 2}, {17, 1}, {499, 1}, {5741, 1}}

FactorInteger[9]

{{3, 2}}

Plot[f[x], {x, -2, 2}, PlotStyle→ Red]

[Graphics:HTMLFiles/index_28.gif]

-Graphics -

c11 = Plot[f[x], {x, -2, 2}, PlotStyle→ {Thickness[0.005], RGBColor[1, 0, 1]}]

[Graphics:HTMLFiles/index_31.gif]

-Graphics -

g[x_] = -x^2 - x + 2

2 - x - x^2

c22 = Plot[g[x], {x, -2, 2}, PlotStyle→ {Thickness[0.005], RGBColor[1, 0, 0]}]

[Graphics:HTMLFiles/index_36.gif]

-Graphics -

Show[c11, c22]

[Graphics:HTMLFiles/index_39.gif]

-Graphics -

Solve[g[x] == 0, x]

{{x→ -2}, {x→1}}

Solve[f[x] == 0, x]

{{x→1/4 (1 - I 7^(1/2))}, {x→1/4 (1 + I 7^(1/2))}}

Solve[f[x] == g[x], x]

{{x→ -1/3^(1/2)}, {x→1/3^(1/2)}}

p11 = Graphics[{PointSize[0.02], Blue, Point[{1/Sqrt[3], f[1/Sqrt[3]]}]}]

-Graphics -

Show[c11, c22, p11]

[Graphics:HTMLFiles/index_50.gif]

-Graphics -

p22 = Graphics[{PointSize[0.02], Blue, Point[{-1/Sqrt[3], f[-1/Sqrt[3]]}]}]

-Graphics -

Show[c11, c22, p11, p22]

[Graphics:HTMLFiles/index_55.gif]

-Graphics -

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