Question

Expand the polynomial f(x) = x² – 3x + 2 in power of x – 1

Answer 1

Let f(x) = x² – 3x + 2

f(x) = x² – 3x + 2, f(1) = 0

f'(x) = 2x – 3, f'(1) = – 1

f”(x) = 2, f”(1) = 2

Taylor series of f(x) is

f(x) = `sum_("n" = 0)^("n" = oo) "a"_"n" (x - 1)^"n"`

Where a_n = `("f"^(("n"))(1))/("n"!)`

∴ The required expansion is

x² – 3x + 2 = `0 - (1(x - 1))/(1!) + (2(x - 1)^2)/(2!)`

= – (x – 1) + (x – 1)²