The value of a is 9.
What is factor?
A factor of polynomial P(x) is any polynomial which divides evenly into P(x).
How to find the solution for a polynomial?
For finding the factor of a polynomial we will perform following steps:
- If f(x) is any polynomial then substitute f(x) = 0.
- Then factorize the given polynomial by splitting the middle term. Then solve for x.
According to the given question.
We have a cubic polynomial [tex]x^{3} -4x^{2} +ax -2a[/tex]
Also, x - 3a is a factor of the given polynomial.
⇒ [tex]x - 3 = 0[/tex]
⇒[tex]x = 3[/tex]
⇒ 3 is the one solution of the given cubic polynomial.
If 3 is the one solution of the cubic polynomial then it must satisfy the equation (i).
So, substitute the value of x in the given polynomial.
[tex](3)^{3} -4(3)^{2} + a (3) - 2a = 0[/tex]
⇒[tex]27 -4(3)^{2} +a(3) -2a=0[/tex]
⇒[tex]27 - 36 + 3a - 2a= 0[/tex]
⇒[tex]-9 + a = 0[/tex]
⇒ [tex]a = 9[/tex]
Therefore, the value of a is 9.
Find out more information about factor and solution of polynomial here:
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