Mister Exam
Factor polynomial z^3+5*z^2+4*z-10
The solution
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3 2 z + 5*z + 4*z - 10
$$\left(4 z + \left(z^{3} + 5 z^{2}\right)\right) - 10$$
z^3 + 5*z^2 + 4*z - 10
General simplification
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3 2 -10 + z + 4*z + 5*z
$$z^{3} + 5 z^{2} + 4 z - 10$$
-10 + z^3 + 4*z + 5*z^2
Factorization
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(x - 1)*(x + 3 + I)*(x + 3 - I)
$$\left(x - 1\right) \left(x + \left(3 + i\right)\right) \left(x + \left(3 - i\right)\right)$$
((x - 1)*(x + 3 + i))*(x + 3 - i)
Combining rational expressions
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-10 + z*(4 + z*(5 + z))
$$z \left(z \left(z + 5\right) + 4\right) - 10$$
-10 + z*(4 + z*(5 + z))
Assemble expression
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3 2 -10 + z + 4*z + 5*z
$$z^{3} + 5 z^{2} + 4 z - 10$$
-10 + z^3 + 4*z + 5*z^2
Rational denominator
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3 2 -10 + z + 4*z + 5*z
$$z^{3} + 5 z^{2} + 4 z - 10$$
-10 + z^3 + 4*z + 5*z^2
Common denominator
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3 2 -10 + z + 4*z + 5*z
$$z^{3} + 5 z^{2} + 4 z - 10$$
-10 + z^3 + 4*z + 5*z^2
Combinatorics
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/ 2 \ (-1 + z)*\10 + z + 6*z/
$$\left(z - 1\right) \left(z^{2} + 6 z + 10\right)$$
(-1 + z)*(10 + z^2 + 6*z)
Trigonometric part
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3 2 -10 + z + 4*z + 5*z
$$z^{3} + 5 z^{2} + 4 z - 10$$
-10 + z^3 + 4*z + 5*z^2