Solution - Simplification or other simple results
Other Ways to Solve
Simplification or other simple resultsStep by Step Solution
Step 1 :
Equation at the end of step 1 :
(((x3) - 4x) - 2x2) - 8
Step 2 :
Checking for a perfect cube :
2.1 x3-2x2-4x-8 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-2x2-4x-8
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -4x-8
Group 2: -2x2+x3
Pull out from each group separately :
Group 1: (x+2) • (-4)
Group 2: (x-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 :
2.3 Find roots (zeroes) of : F(x) = x3-2x2-4x-8
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 -8.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4 ,8
Let us test ....
| P | Q | P/Q | F(P/Q) | Divisor | |||||
|---|---|---|---|---|---|---|---|---|---|
| -1 | 1 | -1.00 | -7.00 | ||||||
| -2 | 1 | -2.00 | -16.00 | ||||||
| -4 | 1 | -4.00 | -88.00 | ||||||
| -8 | 1 | -8.00 | -616.00 | ||||||
| 1 | 1 | 1.00 | -13.00 | ||||||
| 2 | 1 | 2.00 | -16.00 | ||||||
| 4 | 1 | 4.00 | 8.00 | ||||||
| 8 | 1 | 8.00 | 344.00 |
Polynomial Roots Calculator found no rational roots
Final result :
x3 - 2x2 - 4x - 8
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