Question

If h left-parenthesis x right-parenthesis equals f left-parenthesis x right-parenthesis times g left-parenthesis x right-parenthesis equals negative x superscript 2 baseline minus 3 ⁢ x plus 4, what are possible equations for f left-parenthesis x right-parenthesis and g left-parenthesis x right-parenthesis

Answer 1

Given
  h(x) = f(x)·g(x) = -x² -3x +4
Find
  Possible equations for f(x) and g(x)

Solution
  h(x) factors as -(x -4)(x +1)
There are an infinite number of possibilities for f(x) and g(x). Some of the simpler ones are ...
  f(x) = 4 -x; g(x) = x +1
or
  f(x) = -x -1; g(x) = x -4
or either of this with f and g swapped.

For some q(x), you can also have ...
  f(x) = (4 -x)×q(x); g(x) = (x +1)/q(x)
again, possibly with f and g swapped