-3x5+2x-1
This solution deals with finding the roots (zeroes) of polynomials.
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Step by Step Solution
Reformatting the input đầu vào :
Changes made lớn your đầu vào should not affect the solution: (1): "x5" was replaced by "x^5".Step 1 :
Equation at the end of step 1 :((0 - 3x5) + 2x) - 1
Step 2 :
Step 3 :
Pulling out like terms :3.1 Pull out like factors:-3x5 + 2x - 1=-1•(3x5 - 2x + 1)Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(x) = 3x5 - 2x + 1Polynomial Roots Calculator is a set of methods aimed at finding values ofxfor which F(x)=0 Rational Roots chạy thử 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 integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then p. Is a factor of the Trailing Constant và Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 3 và the Trailing Constant is 1. The factor(s) are: of the Leading Coefficient : 1,3 of the Trailing Constant : 1 Let us kiểm tra ....
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| -1 | 1 | -1.00 | 0.00 | x + 1 | |||||
| -1 | 3 | -0.33 | 1.65 | ||||||
| 1 | 1 | 1.00 | 2.00 | ||||||
| 1 | 3 | 0.33 | 0.35 |
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p note that q and phường originate from P/Q reduced khổng lồ its lowest terms In our case this means that 3x5 - 2x + 1can be divided with x + 1
Polynomial Long Division :
3.3 Polynomial Long Division Dividing : 3x5 - 2x + 1("Dividend") By:x + 1("Divisor")
| dividend | 3x5 | - | 2x | + | 1 | ||||||||
| -divisor | * 3x4 | 3x5 | + | 3x4 | |||||||||
| remainder | - | 3x4 | - | 2x | + | 1 | |||||||
| -divisor | * -3x3 | - | 3x4 | - | 3x3 | ||||||||
| remainder | 3x3 | - | 2x | + | 1 | ||||||||
| -divisor | * 3x2 | 3x3 | + | 3x2 | |||||||||
| remainder | - | 3x2 | - | 2x | + | 1 | |||||||
| -divisor | * -3x1 | - | 3x2 | - | 3x | ||||||||
| remainder | x | + | 1 | ||||||||||
| -divisor | * x0 | x | + | 1 | |||||||||
| remainder | 0 |
Quotient : 3x4-3x3+3x2-3x+1 Remainder: 0
Polynomial Roots Calculator :
3.4 Find roots (zeroes) of : F(x) = 3x4-3x3+3x2-3x+1See theory in step 3.2 In this case, the Leading Coefficient is 3 và the Trailing Constant is 1. The factor(s) are: of the Leading Coefficient : 1,3 of the Trailing Constant : 1 Let us thử nghiệm ....
| -1 | 1 | -1.00 | 13.00 | ||||||
| -1 | 3 | -0.33 | 2.48 | ||||||
| 1 | 1 | 1.00 | 1.00 | ||||||
| 1 | 3 | 0.33 | 0.26 |
Polynomial Roots Calculator found no rational roots