factorise:-a^3-18a^2+108a-216
Answer it fast please please
Answers
Answer:
(a - 6)^3
Step-by-step explanation:
Given,
a^3 - 18a^2 + 108a - 216
F(a) = a^3-18a^2+108a-216
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 -216.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,2 ,3 ,4 ,6 ,8 ,9 ,12 ,18 ,24 , etc.
In our case this means that
a^3-18a^2+108a-216
can be divided with a-6 .
On dividing a^3-18a^2+108a-216 by (a-6), we get a^2 - 12a + 36.
So now,
p(x) = a^2 - 12a + 36.
On splitting the middle term, we get,
a^2 - 6a - 6a + 36 = 0
=> a(a - 6) -6(a - 6) = 0
=> (a - 6)(a - 6) = 0
Here, either (a - 6) or (a - 6) is equal to zero.
=> (a - 6) = 0 or (a - 6) = 0
So,
=> a = 6 or 6
=> a = 6
Thus by multiplying exponentials, we get, (a - 6)^3.
a^3 - 18a^2 + 108a - 216 = (a - 6)^3
Answer:फा इ स् छु tha tej tee J dhun hai chht
Step-by-step explanation: