Graph each polynomial function. Factor first if the expression is not in factored form. f(x)=x^{2}(x-5)(x+3)(x-1)

${\displaystyle f\left(x\right)=x^2(x-5)(x+3)(x-1)}$ The function in factored form The function has four zeros 0,5,-3 and 1. So, the graph of f(x) crossed the x-axis at (0,0), (5,0),(-3,0), and (1,0) To find the y-intercept, substitute 0 for x in f(x) ${\displaystyle f\left(x\right)=x^2(x-5)(x+3)(x-1)}$
${\displaystyle f\left(0\right)=0^2(0-5)(0+3)(0-1)}$ Substitute 0 for x
${\displaystyle =0}$ So, the function f(x) crosses the y-axis at (0,0) Step 2 $x^2\cdot x\cdot x\cdot x=x^5$ The leading coefficient is 1 Since the leading coefficient is positive and the function f(x) of degree 5 (odd degree) So, the end behavior is ${\displaystyle x\to \mathrm{\infty },f\left(x\right)\to \mathrm{\infty }}$
${\displaystyle x\to -\mathrm{\infty },f\left(x\right)\to -\mathrm{\infty }}$

See the graph below