Mister Exam
Factor polynomial x^7-4*x^5+6*x^3-4*x
The solution
You have entered
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7 5 3 x - 4*x + 6*x - 4*x
$$- 4 x + \left(6 x^{3} + \left(x^{7} - 4 x^{5}\right)\right)$$
x^7 - 4*x^5 + 6*x^3 - 4*x
General simplification
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/ 6 4 2\ x*\-4 + x - 4*x + 6*x /
$$x \left(x^{6} - 4 x^{4} + 6 x^{2} - 4\right)$$
x*(-4 + x^6 - 4*x^4 + 6*x^2)
Factorization
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/ ___\ / ___\ / _______\ / _______\ / _______\ / _______\ x*\x + \/ 2 /*\x - \/ 2 /*\x + \/ 1 - I /*\x - \/ 1 - I /*\x + \/ 1 + I /*\x - \/ 1 + I /
$$x \left(x + \sqrt{2}\right) \left(x - \sqrt{2}\right) \left(x + \sqrt{1 - i}\right) \left(x - \sqrt{1 - i}\right) \left(x + \sqrt{1 + i}\right) \left(x - \sqrt{1 + i}\right)$$
(((((x*(x + sqrt(2)))*(x - sqrt(2)))*(x + sqrt(1 - i)))*(x - sqrt(1 - i)))*(x + sqrt(1 + i)))*(x - sqrt(1 + i))
Rational denominator
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7 5 3 x - 4*x - 4*x + 6*x
$$x^{7} - 4 x^{5} + 6 x^{3} - 4 x$$
x^7 - 4*x - 4*x^5 + 6*x^3
Assemble expression
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7 5 3 x - 4*x - 4*x + 6*x
$$x^{7} - 4 x^{5} + 6 x^{3} - 4 x$$
x^7 - 4*x - 4*x^5 + 6*x^3
Common denominator
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7 5 3 x - 4*x - 4*x + 6*x
$$x^{7} - 4 x^{5} + 6 x^{3} - 4 x$$
x^7 - 4*x - 4*x^5 + 6*x^3
Combinatorics
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/ 2\ / 4 2\ x*\-2 + x /*\2 + x - 2*x /
$$x \left(x^{2} - 2\right) \left(x^{4} - 2 x^{2} + 2\right)$$
x*(-2 + x^2)*(2 + x^4 - 2*x^2)
Trigonometric part
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7 5 3 x - 4*x - 4*x + 6*x
$$x^{7} - 4 x^{5} + 6 x^{3} - 4 x$$
x^7 - 4*x - 4*x^5 + 6*x^3
Powers
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7 5 3 x - 4*x - 4*x + 6*x
$$x^{7} - 4 x^{5} + 6 x^{3} - 4 x$$
x^7 - 4*x - 4*x^5 + 6*x^3
Combining rational expressions
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/ 2 / 2 / 2\\\ x*\-4 + x *\6 + x *\-4 + x ///
$$x \left(x^{2} \left(x^{2} \left(x^{2} - 4\right) + 6\right) - 4\right)$$
x*(-4 + x^2*(6 + x^2*(-4 + x^2)))