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 ....
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")
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