-3x5+2x-1

This solution deals with finding the roots (zeroes) of polynomials.

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Step by Step Solution

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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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PQP/QF(P/Q)Divisor
-11 -1.00 0.00x + 1
-13 -0.33 1.65
11 1.00 2.00
13 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")

dividend3x5-2x+1
-divisor* 3x43x5+3x4
remainder-3x4-2x+1
-divisor* -3x3-3x4-3x3
remainder3x3-2x+1
-divisor* 3x23x3+3x2
remainder-3x2-2x+1
-divisor* -3x1-3x2-3x
remainderx+1
-divisor* x0x+1
remainder0

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 ....

PQP/QF(P/Q)Divisor
-11 -1.00 13.00
-13 -0.33 2.48
11 1.00 1.00
13 0.33 0.26

Polynomial Roots Calculator found no rational roots