Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
(2•3a2) + 27
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
6a2 + 27 = 3 • (2a2 + 9)
Polynomial Roots Calculator :
3.2 Find roots (zeroes) of : F(a) = 2a2 + 9
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 2 and the Trailing Constant is 9.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1 ,3 ,9
Let us test ....
| P | Q | P/Q | F(P/Q) | Divisor | |||||
|---|---|---|---|---|---|---|---|---|---|
| -1 | 1 | -1.00 | 11.00 | ||||||
| -1 | 2 | -0.50 | 9.50 | ||||||
| -3 | 1 | -3.00 | 27.00 | ||||||
| -3 | 2 | -1.50 | 13.50 | ||||||
| -9 | 1 | -9.00 | 171.00 | ||||||
| -9 | 2 | -4.50 | 49.50 | ||||||
| 1 | 1 | 1.00 | 11.00 | ||||||
| 1 | 2 | 0.50 | 9.50 | ||||||
| 3 | 1 | 3.00 | 27.00 | ||||||
| 3 | 2 | 1.50 | 13.50 | ||||||
| 9 | 1 | 9.00 | 171.00 | ||||||
| 9 | 2 | 4.50 | 49.50 |
Polynomial Roots Calculator found no rational roots
Final result :
3 • (2a2 + 9)
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