Mister Exam
Factor polynomial z^3-9*z^2+16*z+26
The solution
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3 2 z - 9*z + 16*z + 26
$$\left(16 z + \left(z^{3} - 9 z^{2}\right)\right) + 26$$
z^3 - 9*z^2 + 16*z + 26
General simplification
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3 2 26 + z - 9*z + 16*z
$$z^{3} - 9 z^{2} + 16 z + 26$$
26 + z^3 - 9*z^2 + 16*z
Factorization
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(x + 1)*(x + -5 + I)*(x + -5 - I)
$$\left(x + 1\right) \left(x + \left(-5 + i\right)\right) \left(x + \left(-5 - i\right)\right)$$
((x + 1)*(x - 5 + i))*(x - 5 - i)
Trigonometric part
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3 2 26 + z - 9*z + 16*z
$$z^{3} - 9 z^{2} + 16 z + 26$$
26 + z^3 - 9*z^2 + 16*z
Common denominator
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3 2 26 + z - 9*z + 16*z
$$z^{3} - 9 z^{2} + 16 z + 26$$
26 + z^3 - 9*z^2 + 16*z
Assemble expression
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3 2 26 + z - 9*z + 16*z
$$z^{3} - 9 z^{2} + 16 z + 26$$
26 + z^3 - 9*z^2 + 16*z
Combining rational expressions
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26 + z*(16 + z*(-9 + z))
$$z \left(z \left(z - 9\right) + 16\right) + 26$$
26 + z*(16 + z*(-9 + z))
Rational denominator
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3 2 26 + z - 9*z + 16*z
$$z^{3} - 9 z^{2} + 16 z + 26$$
26 + z^3 - 9*z^2 + 16*z
Combinatorics
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/ 2 \ (1 + z)*\26 + z - 10*z/
$$\left(z + 1\right) \left(z^{2} - 10 z + 26\right)$$
(1 + z)*(26 + z^2 - 10*z)