Mister Exam
Factor polynomial -x^7+x^6/4+9*x^5/8-9*x^4/32-x^3/8+x^2/32
The solution
You have entered
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6 5 4 3 2
7 x 9*x 9*x x x
- x + -- + ---- - ---- - -- + --
4 8 32 8 32
$$\frac{x^{2}}{32} + \left(- \frac{x^{3}}{8} + \left(- \frac{9 x^{4}}{32} + \left(\frac{9 x^{5}}{8} + \left(- x^{7} + \frac{x^{6}}{4}\right)\right)\right)\right)$$
-x^7 + x^6/4 + (9*x^5)/8 - 9*x^4/32 - x^3/8 + x^2/32
Fraction decomposition
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-x^7 - 9*x^4/32 - x^3/8 + x^6/4 + x^2/32 + 9*x^5/8
$$- x^{7} + \frac{x^{6}}{4} + \frac{9 x^{5}}{8} - \frac{9 x^{4}}{32} - \frac{x^{3}}{8} + \frac{x^{2}}{32}$$
4 3 6 2 5
7 9*x x x x 9*x
- x - ---- - -- + -- + -- + ----
32 8 4 32 8
General simplification
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2 / 5 2 4 3\
x *\1 - 32*x - 9*x - 4*x + 8*x + 36*x /
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32
$$\frac{x^{2} \left(- 32 x^{5} + 8 x^{4} + 36 x^{3} - 9 x^{2} - 4 x + 1\right)}{32}$$
x^2*(1 - 32*x^5 - 9*x^2 - 4*x + 8*x^4 + 36*x^3)/32
Factorization
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/ ___\ / ___\
| \/ 2 | | \/ 2 |
(x + 1)*x*(x - 1/4)*(x - 1)*|x + -----|*|x - -----|
\ 4 / \ 4 /
$$x \left(x + 1\right) \left(x - \frac{1}{4}\right) \left(x - 1\right) \left(x + \frac{\sqrt{2}}{4}\right) \left(x - \frac{\sqrt{2}}{4}\right)$$
(((((x + 1)*x)*(x - 1/4))*(x - 1))*(x + sqrt(2)/4))*(x - sqrt(2)/4)
Numerical answer
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-x^7 + 0.03125*x^2 + 0.25*x^6 + 1.125*x^5 - 0.125*x^3 - 0.28125*x^4
-x^7 + 0.03125*x^2 + 0.25*x^6 + 1.125*x^5 - 0.125*x^3 - 0.28125*x^4
Assemble expression
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4 3 6 2 5
7 9*x x x x 9*x
- x - ---- - -- + -- + -- + ----
32 8 4 32 8
$$- x^{7} + \frac{x^{6}}{4} + \frac{9 x^{5}}{8} - \frac{9 x^{4}}{32} - \frac{x^{3}}{8} + \frac{x^{2}}{32}$$
-x^7 - 9*x^4/32 - x^3/8 + x^6/4 + x^2/32 + 9*x^5/8
Common denominator
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4 3 6 2 5
7 9*x x x x 9*x
- x - ---- - -- + -- + -- + ----
32 8 4 32 8
$$- x^{7} + \frac{x^{6}}{4} + \frac{9 x^{5}}{8} - \frac{9 x^{4}}{32} - \frac{x^{3}}{8} + \frac{x^{2}}{32}$$
-x^7 - 9*x^4/32 - x^3/8 + x^6/4 + x^2/32 + 9*x^5/8
Combining rational expressions
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2
x *(1 + x*(-4 + x*(-9 + 4*x*(9 + 2*x*(1 - 4*x)))))
--------------------------------------------------
32
$$\frac{x^{2} \left(x \left(x \left(4 x \left(2 x \left(1 - 4 x\right) + 9\right) - 9\right) - 4\right) + 1\right)}{32}$$
x^2*(1 + x*(-4 + x*(-9 + 4*x*(9 + 2*x*(1 - 4*x)))))/32
Combinatorics
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2 / 2\
-x *(1 + x)*(-1 + x)*(-1 + 4*x)*\-1 + 8*x /
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32
$$- \frac{x^{2} \left(x - 1\right) \left(x + 1\right) \left(4 x - 1\right) \left(8 x^{2} - 1\right)}{32}$$
-x^2*(1 + x)*(-1 + x)*(-1 + 4*x)*(-1 + 8*x^2)/32
Trigonometric part
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4 3 6 2 5
7 9*x x x x 9*x
- x - ---- - -- + -- + -- + ----
32 8 4 32 8
$$- x^{7} + \frac{x^{6}}{4} + \frac{9 x^{5}}{8} - \frac{9 x^{4}}{32} - \frac{x^{3}}{8} + \frac{x^{2}}{32}$$
-x^7 - 9*x^4/32 - x^3/8 + x^6/4 + x^2/32 + 9*x^5/8
Rational denominator
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7 4 3 2 6 5
- 8192*x - 2304*x - 1024*x + 256*x + 2048*x + 9216*x
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8192
$$\frac{- 8192 x^{7} + 2048 x^{6} + 9216 x^{5} - 2304 x^{4} - 1024 x^{3} + 256 x^{2}}{8192}$$
(-8192*x^7 - 2304*x^4 - 1024*x^3 + 256*x^2 + 2048*x^6 + 9216*x^5)/8192
Powers
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4 3 6 2 5
7 9*x x x x 9*x
- x - ---- - -- + -- + -- + ----
32 8 4 32 8
$$- x^{7} + \frac{x^{6}}{4} + \frac{9 x^{5}}{8} - \frac{9 x^{4}}{32} - \frac{x^{3}}{8} + \frac{x^{2}}{32}$$
-x^7 - 9*x^4/32 - x^3/8 + x^6/4 + x^2/32 + 9*x^5/8