### ((3x-4x^(3)+6x^(4)+1))/(x+3)

This solution giao dịch with simplification or other simple results.

## Step by Step Solution ## Step 1 :

Equation at the end of step 1 :

## Step 2 :

Equation at the over of step 2 :

## Step 3 :

6x4 - 4x3 + 3x + 1 Simplify —————————————————— x + 3 Checking for a perfect cube :3.16x4 - 4x3 + 3x + 1 is not a perfect cube

Trying to lớn factor by pulling out :

3.2 Factoring: 6x4 - 4x3 + 3x + 1 Thoughtfully split the expression at hand into groups, each group having two terms:Group 1: 3x + 1Group 2: 6x4 - 4x3Pull out from each group separately :Group 1: (3x + 1) • (1)Group 2: (3x - 2) • (2x3)Bad news !! Factoring by pulling out fails : The groups have no common factor & can not be added up to size a multiplication.

### Polynomial Roots Calculator :

3.3 Find roots (zeroes) of : F(x) = 6x4 - 4x3 + 3x + 1Polynomial Roots Calculator is a phối 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 and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 6 và the Trailing Constant is 1. The factor(s) are: of the Leading Coefficient : 1,2 ,3 ,6 of the Trailing Constant : 1 Let us test ....

PQP/QF(P/Q)Divisor
-11 -1.00 8.00
-12 -0.50 0.38
-13 -0.33 0.22
-16 -0.17 0.52
11 1.00 6.00
12 0.50 2.38
13 0.33 1.93
16 0.17 1.49

Polynomial Roots Calculator found no rational roots

### Polynomial Long Division :

3.4 Polynomial Long Division Dividing : 6x4 - 4x3 + 3x + 1("Dividend") By:x + 3("Divisor")

 dividend 6x4 - 4x3 + 3x + 1 -divisor * 6x3 6x4 + 18x3 remainder - 22x3 + 3x + 1 -divisor * -22x2 - 22x3 - 66x2 remainder 66x2 + 3x + 1 -divisor * 66x1 66x2 + 198x remainder - 195x + 1 -divisor * -195x0 - 195x - 585 remainder 586

Quotient : 6x3 - 22x2 + 66x - 195 Remainder : 586

## Final result :

6x4 - 4x3 + 3x + 1 —————————————————— x + 3 See results of polynomial long division: 1. In step #03.04