Question 953542
The function f is a fifth-degree polynomial with
the x-intercepts -4, 1, and 7,
y-intercept 112 and
f (x) ≥ 0 for x ≤ 7 
:
We have the three factors (x+4)(x-1)(x-7), the y intercept 4 * 1 * 7 = 28 not 112.
28 goes into 112 4 times so lets change the factors to (x+4)(x-1)(4x-28)
4x + 28 = 0; x still equal -7
but now we can construct the equation
FOIL(x+4)(x-1) = x^2 + 3x - 4 
:
x^2 + 3x - 4
 X (4x - 28)
-------------
4x^3 - 16x^2 - 100x + 112 but this only a third degree equation but satisfies the requirements
{{{ graph( 300, 200, -10, 10, -200, 250, 4x^3 - 16x^2 - 100x + 112, 112) }}}
Green line is y=112