Turn polynomial into another form by using synthetic division

Question

$$f(x) = 8(x-\frac{1}{2})^3+16(x-\frac{1}{2})^2+6(x-\frac{1}{2})+7$$ How do I turn the above polynomial into the form shown below by using synthetic division? $$f(x) = a(2x-1)^3+b(2x-1)^2+c(2x-1)+d$$

And also how do I solve for a, b, c, d?

Answer 1

use that $$x-\frac{1}{2}=\frac{2x-1}{2}$$ and so on and $$\frac{(2x-1)^3}{2^3}=\frac{(2x-1)^3}{8}$$