Answer:
x4 - 3x3 + 5x - 6
————————
x + 2
Explanation:
Step 1 :
((((x4) - 3x3) + 5x) - 6) • (x + 2)(-1)
Step 2
Checking for a perfect cube :
x4-3x3+5x-6 is not a perfect cube
Trying to factor by pulling out :
Factoring: x4-3x3+5x-6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 5x-6
Group 2: x4-3x3
Pull out from each group separately :
Group 1: (5x-6) • (1)
Group 2: (x-3) • (x3)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Find roots (zeroes) of : F(x) = x4-3x3+5x-6
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test 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 integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is -6.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,6
Final result :
x4 - 3x3 + 5x - 6
————————
x + 2