Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - 5.9 Exercises - Skill Practice - Page 397: 8

$f(x)=-\dfrac{1}{6}(x+3)(x-1)(x-4)$

Here, we have $f(x)=a (x-(-3))(x-1)(x-4)$ or, $f(x)=a (x+3)(x-1)(x-4)$ When $x=3$, then we have $2=a(3+3)(3-1)(3-4)$ or, $-12a=2$ This gives: $a=-\dfrac{1}{6}$ Thus, we have $f(x)=-\dfrac{1}{6}(x+3)(x-1)(x-4)$