Algebra 2 help !!!!!!!!!!

i'm really stuck on this question...if anyone can explain it i would really appreciate it!!!!

write a polynomial function whose graph has the given x intercepts and has a leading coefficient of 1
(-3,0) (0,0) (5,0)

x intercepts
(-3,0) (0,0) (5,0)

rewrite
x = -3
x = 0
x = 5

rewrite
x + 3 = 0
x = 0
x - 5 = 0


If we multiply these we get a function
(x + 3)(x)(x - 5)
x(x + 3)(x - 5)
x(x² - 5x + 3x - 15)
x( x² - 2x - 15)

x³ - 2x² - 15 x

so this is you function
y = x³ - 2x² - 15 x
or
f(x) = x³ - 2x² - 15 x


I hope this is what you want, and it helps!!!

Since the polynomial passes through 0,0 or Origin, then x is common throughout the polynomial.
Next, Since there are 3, x intercepts, the polynomial is a 3 degree equation in x.
x we have taken common,
since the polynomial passes through (-3,0), then -3 is a solution to the polynomial, so by remainder theorem, (x+3) is also a factor of the polynomial
Similarly (x-5) is also a factor of the polynomial
Your required polynomial is x(x+3)(x-5)
x^3-2x^2-15x
This is the required polynomial since the leading co-efficient is 1, and our polynomial also has leading co-efficient 1, we leave this as it is.