### 3x5-7x4+6x2-14x

This deals with factoring binomials as the sum or difference of cubes.

## Step by step Solution

### Reformatting the entry :

Changes make to your input need to not affect the solution: (1): "x2" was changed by "x^2". 2 an ext similar replacement(s).## Step 1 :

Equation at the finish of step 1 :(((3•(x5))-(7•(x4)))+(2•3x2))-14x

## step 2 :

Equation in ~ the finish of step 2 : (((3 • (x5)) - 7x4) + (2•3x2)) - 14x## step 3 :

Equation at the finish of step 3 : ((3x5 - 7x4) + (2•3x2)) - 14x## Step 4 :

## Step 5 :

Pulling out choose terms :5.1 pull out prefer factors:3x5 - 7x4 + 6x2 - 14x=x•(3x4 - 7x3 + 6x - 14)Checking because that a perfect cube :5.23x4 - 7x3 + 6x - 14 is not a perfect cube

Trying to variable by pulling out :5.3 Factoring: 3x4 - 7x3 + 6x - 14 Thoughtfully break-up the expression at hand into groups, each group having two terms:Group 1: 6x - 14Group 2: 3x4 - 7x3Pull the end from each team separately :Group 1: (3x - 7) • (2)Group 2: (3x - 7) • (x3) -------------------Add up the 2 groups:(3x - 7) • (x3 + 2)Which is the desired factorization

Trying to element as a sum of Cubes:5.4 Factoring: x3 + 2 Theory:A amount of two perfect cubes, a3+b3 have the right to be factored into :(a+b)•(a2-ab+b2)Proof: (a+b)•(a2-ab+b2) = a3-a2b+ab2+ba2-b2a+b3=a3+(a2b-ba2)+(ab2-b2a)+b3=a3+0+0+b3=a3+b3Check: 2 is no a cube !! Ruling:Binomial can not it is in factored as the difference of 2 perfect cubes

### Polynomial root Calculator :

5.5 find roots (zeroes) that : F(x) = x3 + 2Polynomial root Calculator is a collection of approaches aimed in ~ finding worths ofxfor i m sorry F(x)=0 Rational root Test is one of the above mentioned tools. It would certainly only find Rational Roots that is number x which deserve to be expressed as the quotient of 2 integersThe Rational source Theorem says that if a polynomial zeroes for a reasonable numberP/Q then p is a factor of the Trailing constant and Q is a variable of the top CoefficientIn this case, the leading Coefficient is 1 and the Trailing continuous is 2. The factor(s) are: the the top Coefficient : 1of the Trailing consistent : 1 ,2 Let us test ....

PQP/QF(P/Q)Divisor-1 | 1 | -1.00 | 1.00 | ||||||

-2 | 1 | -2.00 | -6.00 | ||||||

1 | 1 | 1.00 | 3.00 | ||||||

2 | 1 | 2.00 | 10.00 |

Polynomial roots Calculator uncovered no rational roots