The leading coefficient is positive, there are two relative maximums, and the function has four linear factors. The constant term is not negative.
Statement A:The leading coefficient is positive.
Answer:True. The leading coefficient of a polynomial function is the coefficient of the term with the highest degree. In the graph shown, the highest degree term is $x^4$, and its coefficient is positive. Therefore, the leading coefficient is positive.
Statement B: The constant term is negative.
Answer: False. The constant term of a polynomial function is the coefficient of the term with the degree 0. In the graph shown, the constant term is positive, since the graph crosses the $y$-axis above the origin. Therefore, the constant term is not negative.
Statement C: It has 2 relative maximums.
Answer: True. A relative maximum of a function is a point where the function is greater than or equal to all of the points in its immediate neighborhood. In the graph shown, there are two points where the function reaches a relative maximum: at $x=-2$ and at $x=2$. Therefore, the function has two relative maximums.
Statement D: It has 4 linear factors.
Answer: True. A linear factor of a polynomial function is a factor of the polynomial that is of the first degree, i.e., in the form of $ax+b$ for some constants $a$ and $b$. By the Factor Theorem, a polynomial function has a linear factor of the form $ax+b$ if and only if $f(b)=0$, where $f$ is the polynomial function. In the graph shown, the function crosses the $x$-axis at four points: at $x=-4$, at $x=-2$, at $x=2$, and at $x=4$. Therefore, the function has four linear factors.
Summary:
Statements A, C, and D are true about the polynomial function in the graph shown. Statement B is false.