Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 18

the zeros are $x=-2/3$ or $x=-1$ and the $x$-intercepts are $(-2/3,0)$ and $(-1,0)$.

By factorization, we have $$ f(x)=3x^2+5x+2=(3x+2)(x+1) .$$ That is, we have $3x+2=0 $ or $x+1=0$. So the zeros are $x=-2/3$ or $x=-1$ and the $x$-intercepts are $(-2/3,0)$ and $(-1,0)$.