x4+2x3-2x2+x-6
This solution deals with finding the roots (zeroes) of polynomials.
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Step by Step Solution
Reformatting the input :
Changes made khổng lồ your đầu vào should not affect the solution: (1): "x2" was replaced by "x^2". 2 more similar replacement(s).Step 1 :
Equation at the over of step 1 :((((x4)+(2•(x3)))-2x2)+x)-6
Step 2 :
Equation at the over of step 2 : ((((x4) + 2x3) - 2x2) + x) - 6Step 3 :
Polynomial Roots Calculator :
3.1 Find roots (zeroes) of : F(x) = x4+2x3-2x2+x-6Polynomial Roots Calculator is a phối of methods aimed at finding values ofxfor which F(x)=0 Rational Roots thử nghiệm 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 1 và the Trailing Constant is -6. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,2 ,3 ,6 Let us thử nghiệm ....Xem thêm: Dàn Ý Phân Tích 2 Phát Hiện Của Nghệ Sĩ Phùng, Văn Mẫu Phân Tích Hai Phát Hiện Của Nghệ Sĩ Phùng
| -1 | 1 | -1.00 | -10.00 | ||||||
| -2 | 1 | -2.00 | -16.00 | ||||||
| -3 | 1 | -3.00 | 0.00 | x+3 | |||||
| -6 | 1 | -6.00 | 780.00 | ||||||
| 1 | 1 | 1.00 | -4.00 | ||||||
| 2 | 1 | 2.00 | 20.00 | ||||||
| 3 | 1 | 3.00 | 114.00 | ||||||
| 6 | 1 | 6.00 | 1656.00 |
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 p. Originate from P/Q reduced to lớn its lowest terms In our case this means that x4+2x3-2x2+x-6can be divided with x+3
Polynomial Long Division :
3.2 Polynomial Long Division Dividing : x4+2x3-2x2+x-6("Dividend") By:x+3("Divisor")
| dividend | x4 | + | 2x3 | - | 2x2 | + | x | - | 6 | ||
| -divisor | * x3 | x4 | + | 3x3 | |||||||
| remainder | - | x3 | - | 2x2 | + | x | - | 6 | |||
| -divisor | * -x2 | - | x3 | - | 3x2 | ||||||
| remainder | x2 | + | x | - | 6 | ||||||
| -divisor | * x1 | x2 | + | 3x | |||||||
| remainder | - | 2x | - | 6 | |||||||
| -divisor | * -2x0 | - | 2x | - | 6 | ||||||
| remainder | 0 |
Quotient : x3-x2+x-2 Remainder: 0
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = x3-x2+x-2See theory in step 3.1 In this case, the Leading Coefficient is 1 and the Trailing Constant is -2. The factor(s) are: of the Leading Coefficient : 1of the Trailing Constant : 1 ,2 Let us test ....
| -1 | 1 | -1.00 | -5.00 | ||||||
| -2 | 1 | -2.00 | -16.00 | ||||||
| 1 | 1 | 1.00 | -1.00 | ||||||
| 2 | 1 | 2.00 | 4.00 |
Polynomial Roots Calculator found no rational roots