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
Accepted Solution
A:
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