x^4-x^3-2x^2-x-1
This solution giao dịch with finding the roots (zeroes) of polynomials.
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Step by Step Solution

Step 1 :
Equation at the over of step 1 : ((((x4)-(x3))-2x2)-x)-1Step 2 :
Polynomial Roots Calculator :
2.1 Find roots (zeroes) of : F(x) = x4-x3-2x2-x-1Polynomial Roots Calculator is a phối of methods aimed at finding values ofxfor which F(x)=0 Rational Roots demo 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 and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 1 và the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 Let us demo ....-1 | 1 | -1.00 | 0.00 | x+1 | |||||
1 | 1 | 1.00 | -4.00 |
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p cảnh báo that q and p.
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Originate from P/Q reduced khổng lồ its lowest terms In our case this means that x4-x3-2x2-x-1can be divided with x+1
Polynomial Long Division :
2.2 Polynomial Long Division Dividing : x4-x3-2x2-x-1("Dividend") By:x+1("Divisor")
dividend | x4 | - | x3 | - | 2x2 | - | x | - | 1 | ||
-divisor | * x3 | x4 | + | x3 | |||||||
remainder | - | 2x3 | - | 2x2 | - | x | - | 1 | |||
-divisor | * -2x2 | - | 2x3 | - | 2x2 | ||||||
remainder | - | x | - | 1 | |||||||
-divisor | * 0x1 | ||||||||||
remainder | - | x | - | 1 | |||||||
-divisor | * -x0 | - | x | - | 1 | ||||||
remainder | 0 |
Quotient : x3-2x2-1 Remainder: 0
Polynomial Roots Calculator :
2.3 Find roots (zeroes) of : F(x) = x3-2x2-1See theory in step 2.1 In this case, the Leading Coefficient is 1 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 Let us thử nghiệm ....
-1 | 1 | -1.00 | -4.00 | ||||||
1 | 1 | 1.00 | -2.00 |
Polynomial Roots Calculator found no rational roots