((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 ....
| -1 | 1 | -1.00 | 8.00 | ||||||
| -1 | 2 | -0.50 | 0.38 | ||||||
| -1 | 3 | -0.33 | 0.22 | ||||||
| -1 | 6 | -0.17 | 0.52 | ||||||
| 1 | 1 | 1.00 | 6.00 | ||||||
| 1 | 2 | 0.50 | 2.38 | ||||||
| 1 | 3 | 0.33 | 1.93 | ||||||
| 1 | 6 | 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