if x-2 is a factor of polynomial x cube - 2ax square + ax - 1 what is the value of a ??
let f(x) = x^3 - 2ax^2 + ax - 1
if x-2 is a factor, then f(2) = 0
f(2) = 8 -8a + 2a - 1 = 0
-6a = -7
a = 7/6
To find the value of a, we need to determine the relationship between the given polynomial and the factor x-2.
A polynomial P(x) is divisible by a factor ax-b if and only if P(b) = 0.
In this case, x-2 is a factor of the polynomial x^3 - 2ax^2 + ax - 1. Therefore, substituting x=2 into the polynomial should yield 0.
Let's substitute x=2 into the polynomial:
P(2) = (2)^3 - 2a(2)^2 + a(2) - 1
= 8 - 8a + 2a - 1
= 7 - 6a
Since we are looking for the value of a where P(2) = 0, we can set up the equation:
7 - 6a = 0
To solve for a, we can isolate the variable by subtracting 7 from both sides:
-6a = -7
Finally, dividing both sides of the equation by -6 gives:
a = 7/6
Therefore, the value of a is 7/6.