Question

Express x^2-8x+5 in the term (x-a)^2-b where a and b are integers

Answer 1

(x-4)² -11 where a = 4, b = 11

Explanation:

The final form (x-a)² - b evaluates to x² - 2ax + a² -b

Matching

x² - 8x + 5

x² - 2ax + a² -b

This gives us -2ax = -8x or -2a = -8 or a = 4

and a² - b = 11 ==> 16 - b = 11 or b =5

Rewritten form is

(x-4)² -11