Answer:
3x3 + 4x2 + 9x + 28
Step-by-step explanation:
Step by Step Solution
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STEP
1
:
Equation at the end of step 1
(((3 • (x3)) + 22x2) + 9x) + 28
STEP
2
:
Equation at the end of step
2
:
((3x3 + 22x2) + 9x) + 28
STEP
3
:
Checking for a perfect cube
3.1 3x3+4x2+9x+28 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 3x3+4x2+9x+28
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 9x+28
Group 2: 3x3+4x2
Pull out from each group separately :
Group 1: (9x+28) • (1)
Group 2: (3x+4) • (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) = 3x3+4x2+9x+28
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 3 and the Trailing Constant is 28.
The factor(s) are:
of the Leading Coefficient : 1,3
of the Trailing Constant : 1 ,2 ,4 ,7 ,14 ,28
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 20.00
-1 3 -0.33 25.33
-2 1 -2.00 2.00
-2 3 -0.67 22.89
-4 1 -4.00 -136.00
Note - For tidiness, printing of 19 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Final result :
3x3 + 4x2 + 9x + 28
