ahemmm having x-intercepts of -3 and -5.. ..well, that simply means, -3 and -5 are roots or solutions or zeros of the equation
it namely means x = -3 and x = -5, an x-intercept is when the graph touches the x-axis, at that point, the y-intercept is 0, so the point is (-3, 0) and (-5, 0)
if the roots are -3, and -5, then
[tex]\bf \begin{cases}
x=-3\implies x+3=0\implies &(x+3)=0\\
x=-5\implies x+5=0\implies &(x+5)=0
\end{cases}\\\\
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(x+3)(x+5)=0\implies (x+3)(x+5)=y\implies x^2+8x+15=y[/tex]
if you have the zeros/x-intercepts/solutions of the polynomial, all you have to do is, get the factors, as above, and get their product, to get the parent original polynomial.
