# Chapter 4 - Polynomial and Rational Functions - 4.1 Polynomial Functions and Models - 4.1 Assess Your Understanding - Page 185: 48

$f(x)=x^4 - 3 x^3 - 15 x^2 + 19 x + 30$.

#### Work Step by Step

If $c$ is a zero of a function with multiplicity $b$ then $(x-c)^b$ is a “factor” of the function. We are given that the degree is $4$, and the zeros are $-3$, $-1$, $2$ and $5$, hence $f(x)=a(x+3)(x+1)(x-2)(x-5)=a(x^4 - 3 x^3 - 15 x^2 + 19 x + 30 ).$ If $a=1$ then the function is $f(x)=x^4 - 3 x^3 - 15 x^2 + 19 x + 30$.

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