Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 185: 55

$f(x)= 5x^4-10x^2+5$

Step 1. Use the given zeros of the polynomial and write a general form $f(x)=a(x+1)^2(x-1)^2$ where $a$ is unknown. Step 2. Use the point on the function to get $f(-2)=a(-2+1)^2(-2-1)^2=45$ which gives $a=5$ Step 3. The function is $f(x)=5(x+1)^2(x-1)^2=5x^4-10x^2+5$