Mister Exam
Other calculators
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How to use it?
- Factor polynomial:
- 1-a+a^2-a^3+a^4-a^5+a^6-a^7+a^8-a^9
- 0.09-a^2
- x^4-9
- a^2+8*a+16
- Least common denominator:
- (-y*exp(1)/(exp(1)+1)+(1-y)*exp(1)/((1-1/(exp(1)+1))*(exp(1)+1)^2))/m
- ((-k2/p)*(k3/(t3*p+1))+k1*p)*((k5*p)/(1+k3*p*(k3/(t3*p+1))*(k4*(t4*p+1))))
- (k1*p*(k4*(t4*p+1))+k2/p)*k5*p+(k1*p)*(k3/(t3*p+1))
- k1/(1+k1*(-k2*k3*k3/((t3^2*s^2+2*t3*s*e+1)*(t2*s+1))+1/(t1*s+1)))
- Factor squared:
- -a^4-8*a^2-1
- -q^4-4*q^2+5
- -9*p^2-5*p-4
- x^2-x*a+4*a^2
- How do you in partial fractions?:
- (6x^2+29x)/(x+5)
- (x^3+12*x)*(x/(2*(x^3+12*x))+(-12-3*x^2)*(x^2+4)/(4*(x^3+12*x)^2))/(x^2+4)
- 3*x^2/(8-x^4)+4*x^6/(8-x^4)^2
- 1/(n*(n+1)*(n+2))
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Identical expressions
- one -a+a^ two -a^ three +a^ four -a^ five +a^ six -a^ seven +a^ eight -a^ nine
- 1 minus a plus a squared minus a cubed plus a to the power of 4 minus a to the power of 5 plus a to the power of 6 minus a to the power of 7 plus a to the power of 8 minus a to the power of 9
- one minus a plus a to the power of two minus a to the power of three plus a to the power of four minus a to the power of five plus a to the power of six minus a to the power of seven plus a to the power of eight minus a to the power of nine
- 1-a+a2-a3+a4-a5+a6-a7+a8-a9
- 1-a+a²-a³+a⁴-a⁵+a⁶-a⁷+a⁸-a⁹
- 1-a+a to the power of 2-a to the power of 3+a to the power of 4-a to the power of 5+a to the power of 6-a to the power of 7+a to the power of 8-a to the power of 9
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Similar expressions
- 1-a+a^2-a^3-a^4-a^5+a^6-a^7+a^8-a^9
- 1-a+a^2-a^3+a^4+a^5+a^6-a^7+a^8-a^9
- 1+a+a^2-a^3+a^4-a^5+a^6-a^7+a^8-a^9
- 1-a+a^2-a^3+a^4-a^5-a^6-a^7+a^8-a^9
- 1-a+a^2-a^3+a^4-a^5+a^6-a^7+a^8+a^9
- 1-a+a^2+a^3+a^4-a^5+a^6-a^7+a^8-a^9
- 1-a-a^2-a^3+a^4-a^5+a^6-a^7+a^8-a^9
- 1-a+a^2-a^3+a^4-a^5+a^6-a^7-a^8-a^9
- 1-a+a^2-a^3+a^4-a^5+a^6+a^7+a^8-a^9
Factor polynomial 1-a+a^2-a^3+a^4-a^5+a^6-a^7+a^8-a^9
The solution
You have entered
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2 3 4 5 6 7 8 9 1 - a + a - a + a - a + a - a + a - a
$$- a^{9} + \left(a^{8} + \left(- a^{7} + \left(a^{6} + \left(- a^{5} + \left(a^{4} + \left(- a^{3} + \left(a^{2} + \left(1 - a\right)\right)\right)\right)\right)\right)\right)\right)$$
1 - a + a^2 - a^3 + a^4 - a^5 + a^6 - a^7 + a^8 - a^9
General simplification
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Factorization
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/ ___________\ / ___________\ / ___________\ / ___________\ / ___________\ / ___________\ / ___________\ / ___________\
| ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ | | ___ / ___ |
| 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 | | 1 \/ 5 / 5 \/ 5 |
(a - 1)*|a + - - ----- + I* / - + ----- |*|a + - - ----- - I* / - + ----- |*|a + - - - ----- + I* / - - ----- |*|a + - - - ----- - I* / - - ----- |*|a + - + ----- + I* / - - ----- |*|a + - + ----- - I* / - - ----- |*|a + - - + ----- + I* / - + ----- |*|a + - - + ----- - I* / - + ----- |
\ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 / \ 4 4 \/ 8 8 /
$$\left(a - 1\right) \left(a + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a + \left(- \frac{\sqrt{5}}{4} + \frac{1}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a + \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(a + \left(- \frac{\sqrt{5}}{4} - \frac{1}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(a + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(a + \left(\frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{5}{8} - \frac{\sqrt{5}}{8}}\right)\right) \left(a + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} + i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right) \left(a + \left(- \frac{1}{4} + \frac{\sqrt{5}}{4} - i \sqrt{\frac{\sqrt{5}}{8} + \frac{5}{8}}\right)\right)$$
((((((((a - 1)*(a + 1/4 - sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(a + 1/4 - sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8)))*(a - 1/4 - sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(a - 1/4 - sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8)))*(a + 1/4 + sqrt(5)/4 + i*sqrt(5/8 - sqrt(5)/8)))*(a + 1/4 + sqrt(5)/4 - i*sqrt(5/8 - sqrt(5)/8)))*(a - 1/4 + sqrt(5)/4 + i*sqrt(5/8 + sqrt(5)/8)))*(a - 1/4 + sqrt(5)/4 - i*sqrt(5/8 + sqrt(5)/8))
Common denominator
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Numerical answer
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1.0 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
1.0 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Combining rational expressions
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Rational denominator
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Combinatorics
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/ 2 3 4\ / 2 4 3\ -(-1 + a)*\1 + a + a + a + a /*\1 + a + a - a - a /
$$- \left(a - 1\right) \left(a^{4} - a^{3} + a^{2} - a + 1\right) \left(a^{4} + a^{3} + a^{2} + a + 1\right)$$
-(-1 + a)*(1 + a + a^2 + a^3 + a^4)*(1 + a^2 + a^4 - a - a^3)
Trigonometric part
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Powers
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9
Assemble expression
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2 4 6 8 3 5 7 9 1 + a + a + a + a - a - a - a - a - a
$$- a^{9} + a^{8} - a^{7} + a^{6} - a^{5} + a^{4} - a^{3} + a^{2} - a + 1$$
1 + a^2 + a^4 + a^6 + a^8 - a - a^3 - a^5 - a^7 - a^9