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

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