Answer:
x4 + 2x2 + 3x + 1
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(((((x4)-(3•(x2)))+4x)+5x2)+1)-x
Step 2 :
Equation at the end of step 2 :
(((((x4)-3x2)+4x)+5x2)+1)-x
Step 3 :
Checking for a perfect cube :
3.1 x4+2x2+3x+1 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: x4+2x2+3x+1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 3x+1
Group 2: x4+2x2
Pull out from each group separately :
Group 1: (3x+1) • (1)
Group 2: (x2+2) • (x2)
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(x) = x4+2x2+3x+1
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 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 1.00
1 1 1.00 7.00
Polynomial Roots Calculator found no rational roots
Final result :
x4 + 2x2 + 3x + 1
Processing ends successfully
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