Chapter 5 - Section 5.1 - Polynomial Functions and Models - 5.1 Assess Your Understanding - Page 340: 118

$f(x)=x^3(x+4)(x-2)$

If $a$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “multiplier” of the function. Hence here $f(x)=kx^3(x+4)(x-2)$ $(-2,64)$ is on the graph thus $k\cdot(-2)^3(2)(-4)=64\\64k=64\\k=1$ So $f(x)=x^3(x+4)(x-2)$