Solution - Simplification or other simple results
Other Ways to Solve
Simplification or other simple resultsStep by Step Solution
Step 1 :
Polynomial Roots Calculator :
1.1 Find roots (zeroes) of : F(x) = x5-22x-40
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -40.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,5 ,8 ,10 ,20 ,40
Let us test ....
| P | Q | P/Q | F(P/Q) | Divisor | |||||
|---|---|---|---|---|---|---|---|---|---|
| -1 | 1 | -1.00 | -19.00 | ||||||
| -2 | 1 | -2.00 | -28.00 | ||||||
| -4 | 1 | -4.00 | -976.00 | ||||||
| -5 | 1 | -5.00 | -3055.00 | ||||||
| -8 | 1 | -8.00 | -32632.00 | ||||||
| -10 | 1 | -10.00 | -99820.00 | ||||||
| -20 | 1 | -20.00 | -3199600.00 | ||||||
| -40 | 1 | -40.00 | -102399160.00 | ||||||
| 1 | 1 | 1.00 | -61.00 | ||||||
| 2 | 1 | 2.00 | -52.00 | ||||||
| 4 | 1 | 4.00 | 896.00 | ||||||
| 5 | 1 | 5.00 | 2975.00 | ||||||
| 8 | 1 | 8.00 | 32552.00 | ||||||
| 10 | 1 | 10.00 | 99740.00 | ||||||
| 20 | 1 | 20.00 | 3199520.00 | ||||||
| 40 | 1 | 40.00 | 102399080.00 |
Polynomial Roots Calculator found no rational roots
Final result :
x5 - 22x - 40
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