Question 1133750

IF [(X-4)^5 -7(X-4)^4 +7(X-4)^3 -7(X-4)^2 +7(X-4)-6=0] FIND THE VALUE OF X....please  help me to solve this problem..as soon as possible...Thank you
<pre>This problem is EXTREMELY easy......easier than you would ever think.
You'll notice that the variable here is actually the binomial X - 4. SO, let X - 4 be a
Then {{{matrix(1,3, (X - 4)^5 -7(X - 4)^4 + 7(X - 4)^3 - 7(X - 4)^2 + 7(X - 4) - 6, "=", 0)}}} becomes: {{{matrix(1,3, a^5 -7a^4 + 7a^3 - 7a^2 + 7a - 6, "=", 0)}}}. 
Now, using the RATIONAL ROOT THEOREM, LONG DIVISION of POLYNOMIALS, or SYNTHETIC DIVISION, and the factors of 6. which are 1, -1, 2, -2, 3, -3, 6, or -6,
we find that: {{{matrix(1,5, f(6), "=", (6)^5 - 7(6)^4 + 7(6)^3 - 7(6)^2 + 7(6) - 6, "=", 0)}}}, and so, 6 is a ROOT of the function: {{{matrix(1,3, a^5 -7a^4 + 7a^3 - 7a^2 + 7a - 6, "=", 0)}}}. 
Since X - 4 = a, and a = 6, we can say that: X - 4 = 6, and so: {{{highlight_green(matrix(1,5, X, "=", 6 + 4, "=", 10))}}}