Question

what is the relationship between x-intercept and zeroes

Answer 1

idk sorry I don't want to give you the wrong answer

Answer 2

What is a polynomial equation?
It is a polynomial set equal to 0. P(x) = 0.
P(x) = 5x3 − 4x2 + 7x − 8 = 0
2. What do we mean by a root, or zero, of a polynomial?
It is a solution to the polynomial equation, P(x) = 0.
It is that value of x that makes the polynomial equal to 0.
In other words, the number r is a root of a polynomial P(x)
if and only if P(r) = 0.
Is this what you are reffering to?

Answer 3

yes

Answer 4

Zeros, solutions, and roots are values of x at which y is 0 (solution -- assuming the equation is something equals 0 and the something represents y).

The x-intercept is the point that represents this on the graph

By factors I assume you mean a polynomial factored into binomial factors.
It is of the form (ax+b)(cx+d)...=0. Such as (x+2)(x-3)=0.
Such factors lead to the solutions or zeros or roots of the equation; you have to set each factor equal to 0 and solve for x for each factor.
The zeros of a polynomial are exactly its roots, i.e., all x-values such that p(x) = 0. Some of the roots may be real, some complex. For those that are real, the roots correspond to the x-intercepts. To get the roots, we use the Fundamental Theorem of Algebra proved (arguably) by Gauss in 1799: we try to factor it into its linear factorization p%28x%29+=+%28x+-+a1%29%28x+-+a2%29...%28x+-+an%29 and equate each factor to zero. (Again some of them may be real, some complex.)