### 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) - 6

## Step 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 ....

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PQP/QF(P/Q)Divisor
-11 -1.00 -10.00
-21 -2.00 -16.00
-31 -3.00 0.00x+3
-61 -6.00 780.00
11 1.00 -4.00
21 2.00 20.00
31 3.00 114.00
61 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 ....

PQP/QF(P/Q)Divisor
-11 -1.00 -5.00
-21 -2.00 -16.00
11 1.00 -1.00
21 2.00 4.00

Polynomial Roots Calculator found no rational roots