a^3-6a+4 Find roots
values.
Answers
Answer:
(a²-2a-2).(a+2)
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "a3" was replaced by "a^3".
STEP
1
:
Polynomial Roots Calculator :
1.1 Find roots (zeroes) of : F(a) = a3-6a-4
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 -4.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,4
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 1.00
-2 1 -2.00 0.00 a+2
-4 1 -4.00 -44.00
1 1 1.00 -9.00
2 1 2.00 -8.00
4 1 4.00 36.00
The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms
In our case this means that
a3-6a-4
can be divided with a+2
Polynomial Long Division :
1.2 Polynomial Long Division
Dividing : a3-6a-4
("Dividend")
By : a+2 ("Divisor")
dividend a3 - 6a - 4
- divisor * a2 a3 + 2a2
remainder - 2a2 - 6a - 4
- divisor * -2a1 - 2a2 - 4a
remainder - 2a - 4
- divisor * -2a0 - 2a - 4
remainder 0
Quotient : a2-2a-2 Remainder: 0