Question

Explain the connection between factors of a polynomial, zeros of a polynomial function, and solutions of a polynomial equation.

Answer 1

Factors of a polynomial, when set equal to zero and solved, become the zeros of a polynomial.

The zeros of a polynomial are the numbers where the y-values are 0 which means the point will lie on the x-axis.

Zeros and solutions are the same things. It is where the graph will cross the x-axis which means the y-value is zero.

I hope this is what you were looking for.

Answer 2

Short answer, they are all the same.

Explanation:

When you factor a polynomial, you get something in the form of (ax + b)(cx + d)... = 0. Using the zero property rule, we know that if the whole thing equals to 0, then each individual factor should equal to 0 as well. And if you set all individual factors to zero like (ax + b) = 0, (cx + d) = 0, ... and solve them, you get the zeros (or solutions) of the polynomial. Another way of solving the zeros of polynomials is to graph them. Instead of setting them to equal to zero, you set them to equal to "y" like (ax + b)(cx + d)...=y and graph the function. Where the function crosses the x-axis are the solutions to the polynomial equation.