Mister Exam
Factor polynomial z^3+5*z^2+17*z+13
The solution
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3 2 z + 5*z + 17*z + 13
$$\left(17 z + \left(z^{3} + 5 z^{2}\right)\right) + 13$$
z^3 + 5*z^2 + 17*z + 13
Factorization
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(x + 1)*(x + 2 + 3*I)*(x + 2 - 3*I)
$$\left(x + 1\right) \left(x + \left(2 + 3 i\right)\right) \left(x + \left(2 - 3 i\right)\right)$$
((x + 1)*(x + 2 + 3*i))*(x + 2 - 3*i)
General simplification
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3 2 13 + z + 5*z + 17*z
$$z^{3} + 5 z^{2} + 17 z + 13$$
13 + z^3 + 5*z^2 + 17*z
Trigonometric part
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3 2 13 + z + 5*z + 17*z
$$z^{3} + 5 z^{2} + 17 z + 13$$
13 + z^3 + 5*z^2 + 17*z
Assemble expression
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3 2 13 + z + 5*z + 17*z
$$z^{3} + 5 z^{2} + 17 z + 13$$
13 + z^3 + 5*z^2 + 17*z
Combining rational expressions
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13 + z*(17 + z*(5 + z))
$$z \left(z \left(z + 5\right) + 17\right) + 13$$
13 + z*(17 + z*(5 + z))
Rational denominator
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3 2 13 + z + 5*z + 17*z
$$z^{3} + 5 z^{2} + 17 z + 13$$
13 + z^3 + 5*z^2 + 17*z
Common denominator
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3 2 13 + z + 5*z + 17*z
$$z^{3} + 5 z^{2} + 17 z + 13$$
13 + z^3 + 5*z^2 + 17*z
Combinatorics
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/ 2 \ (1 + z)*\13 + z + 4*z/
$$\left(z + 1\right) \left(z^{2} + 4 z + 13\right)$$
(1 + z)*(13 + z^2 + 4*z)