Answer:
Final result :
(sorry if this is long)
a3 - 5a2 + 4a + 5
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((4a-(a3))-3)+(((2•(a3))-5a2)+8)
Step 2 :
Equation at the end of step 2 :
((4a-(a3))-3)+((2a3-5a2)+8)
Step 3 :
Checking for a perfect cube :
3.1 a3-5a2+4a+5 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: a3-5a2+4a+5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 4a+5
Group 2: a3-5a2
Pull out from each group separately :
Group 1: (4a+5) • (1)
Group 2: (a-5) • (a2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(a) = a3-5a2+4a+5
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a 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 5.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,5
Hope it helps!!