p1_mrg_algebra1

2890 days ago by LAC2011

factor(x**2+2*x+2) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x + 2
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x + 2
factor(x**2+2*x+1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 1\right)}^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 1\right)}^{2}
factor(x**2+2*x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 2\right)} x
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 2\right)} x
factor(x**2+2*x-1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x - 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x - 1
factor(10*x**2+11*x-6) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(2 \, x + 3\right)} {\left(5 \, x - 2\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(2 \, x + 3\right)} {\left(5 \, x - 2\right)}
factor(x**2-4) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 2\right)} {\left(x + 2\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 2\right)} {\left(x + 2\right)}
factor(x**3-1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 1\right)} {\left(x^{2} + x + 1\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x - 1\right)} {\left(x^{2} + x + 1\right)}
factor(x**3+1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 1\right)} {\left(x^{2} - x + 1\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x + 1\right)} {\left(x^{2} - x + 1\right)}
factor(27*x**3-64) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(3 \, x - 4\right)} {\left(9 \, x^{2} + 12 \, x + 16\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(3 \, x - 4\right)} {\left(9 \, x^{2} + 12 \, x + 16\right)}
var('y') factor(125*x**3+8*y**3) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(5 \, x + 2 \, y\right)} {\left(25 \, x^{2} - 10 \, x y + 4 \, y^{2}\right)}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(5 \, x + 2 \, y\right)} {\left(25 \, x^{2} - 10 \, x y + 4 \, y^{2}\right)}
#factor(x**999-y**999) 
       
factor(123456789011112131415) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}3 \cdot 5 \cdot 19 \cdot 41 \cdot 10565407703133259
\newcommand{\Bold}[1]{\mathbf{#1}}3 \cdot 5 \cdot 19 \cdot 41 \cdot 10565407703133259
factor(2**127-1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}170141183460469231731687303715884105727
\newcommand{\Bold}[1]{\mathbf{#1}}170141183460469231731687303715884105727
solve(x**2+2*x+2==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-i - 1\right), x = \left(i - 1\right)\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-i - 1\right), x = \left(i - 1\right)\right]
solve(x**2+2*x+1==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-1\right)\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-1\right)\right]
solve(x**2+2*x==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-2\right), x = 0\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-2\right), x = 0\right]
solve(x**2+2*x-1==0,x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{2} - 1, x = \sqrt{2} - 1\right]
\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\sqrt{2} - 1, x = \sqrt{2} - 1\right]
plot((x**2+2*x+2,x**2+2*x+1,x**2+2*x,x**2+2*x-1),(-3,2)) 
       
n(-1-sqrt(2)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}-2.41421356237309
\newcommand{\Bold}[1]{\mathbf{#1}}-2.41421356237309
n(-1+sqrt(2)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}0.414213562373095
\newcommand{\Bold}[1]{\mathbf{#1}}0.414213562373095
for i in range(0,9): show(expand((x+1)**i)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}1
\newcommand{\Bold}[1]{\mathbf{#1}}x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} + 3 \, x^{2} + 3 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{5} + 5 \, x^{4} + 10 \, x^{3} + 10 \, x^{2} + 5 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{6} + 6 \, x^{5} + 15 \, x^{4} + 20 \, x^{3} + 15 \, x^{2} + 6 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{7} + 7 \, x^{6} + 21 \, x^{5} + 35 \, x^{4} + 35 \, x^{3} + 21 \, x^{2} + 7 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{8} + 8 \, x^{7} + 28 \, x^{6} + 56 \, x^{5} + 70 \, x^{4} + 56 \, x^{3} + 28 \, x^{2} + 8 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}1
\newcommand{\Bold}[1]{\mathbf{#1}}x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{2} + 2 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{3} + 3 \, x^{2} + 3 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{4} + 4 \, x^{3} + 6 \, x^{2} + 4 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{5} + 5 \, x^{4} + 10 \, x^{3} + 10 \, x^{2} + 5 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{6} + 6 \, x^{5} + 15 \, x^{4} + 20 \, x^{3} + 15 \, x^{2} + 6 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{7} + 7 \, x^{6} + 21 \, x^{5} + 35 \, x^{4} + 35 \, x^{3} + 21 \, x^{2} + 7 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{8} + 8 \, x^{7} + 28 \, x^{6} + 56 \, x^{5} + 70 \, x^{4} + 56 \, x^{3} + 28 \, x^{2} + 8 \, x + 1
f(x)=expand((x+1)**6);f(x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{6} + 6 \, x^{5} + 15 \, x^{4} + 20 \, x^{3} + 15 \, x^{2} + 6 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{6} + 6 \, x^{5} + 15 \, x^{4} + 20 \, x^{3} + 15 \, x^{2} + 6 \, x + 1
f(-1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}0
expand(factor(f(x))/(x+1)) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}x^{5} + 5 \, x^{4} + 10 \, x^{3} + 10 \, x^{2} + 5 \, x + 1
\newcommand{\Bold}[1]{\mathbf{#1}}x^{5} + 5 \, x^{4} + 10 \, x^{3} + 10 \, x^{2} + 5 \, x + 1
f(x).diff().diff().diff().diff().diff().diff().diff() 
       
\newcommand{\Bold}[1]{\mathbf{#1}}0
\newcommand{\Bold}[1]{\mathbf{#1}}0
g(x)=f(x).diff(2) g(1) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}480
\newcommand{\Bold}[1]{\mathbf{#1}}480
f(x).integrate(x).integrate(x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{56} \, x^{8} + \frac{1}{7} \, x^{7} + \frac{1}{2} \, x^{6} + x^{5} + \frac{5}{4} \, x^{4} + x^{3} + \frac{1}{2} \, x^{2}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{1}{56} \, x^{8} + \frac{1}{7} \, x^{7} + \frac{1}{2} \, x^{6} + x^{5} + \frac{5}{4} \, x^{4} + x^{3} + \frac{1}{2} \, x^{2}
f(x).integrate(0,1) 
       
__main__:1: DeprecationWarning: Variable of integration should be
specified explicitly.
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{127}{7}
__main__:1: DeprecationWarning: Variable of integration should be specified explicitly.
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{127}{7}
h(x)=(x+1)/(x**2+x-2) show(factor(h(x))) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x + 1}{{\left(x - 1\right)} {\left(x + 2\right)}}
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{x + 1}{{\left(x - 1\right)} {\left(x + 2\right)}}
h(x).integrate(x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2}{3} \, \log\left(x - 1\right) + \frac{1}{3} \, \log\left(x + 2\right)
\newcommand{\Bold}[1]{\mathbf{#1}}\frac{2}{3} \, \log\left(x - 1\right) + \frac{1}{3} \, \log\left(x + 2\right)
f(x)=x**2*e^(x) f(x).integrate(x) 
       
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{2} - 2 \, x + 2\right)} e^{x}
\newcommand{\Bold}[1]{\mathbf{#1}}{\left(x^{2} - 2 \, x + 2\right)} e^{x}