Given that 2𝑥 – 1is a factor of 𝑥^3 -3x^2 + bx - b which theorem is used to determine the value of b algebraically. Then, list the possible values of the rational zeros of the function.

Answer 1

ax^n + ... + b has rational roots of the form p/q where p is a factor of a, and q is a factor of b.
In this case, all rational roots will be factors of b

If 2x-1 is a factor, then x = 1/2 is a root. The Remainder Theorem says that f(1/2) will have remainder zero. So plug in x = 1/2 and see what b must be.