SOLUTION: what is the relationship between the zeros of a polynomial, the x-intercepts of the graph of that polynomial, and its factors of the form (x-a)? can you also give me an example to

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what is the relationship between the zeros of a polynomial, the x-intercepts of the graph of that polynomial, and its factors of the form (x-a)? can you also give me an example to       Log On


   

Question 371708: what is the relationship between the zeros of a polynomial, the x-intercepts of the graph of that polynomial, and its factors of the form (x-a)? can you also give me an example to better my understanding.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
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.)