Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 185: 56

$f(x)= 3x^5-12x^4-6x^3+36x^2+27x$

Step 1. Use the given zeros of the polynomial and write a general form $f(x)=a(x+1)^2(x)(x-3)^2$ where $a$ is unknown. Step 2. Use the point on the function to get $f(1)=a(1+1)^2(1)(1-3)^2=48$ which gives $a=3$ Step 3. The function is $f(x)=3(x+1)^2(x)(x-3)^2=3x^5-12x^4-6x^3+36x^2+27x$