Answer:
Factors, zeros, solutions, and x-intercepts are all related to the roots of a single polynomial equation.
Step-by-step explanation:
A factor of a polynomial is an expression that divides the polynomial evenly, with no remainder. For example, (x - 3) is a factor of the polynomial x^2 - 5x + 6, because (x^2 - 5x + 6) / (x - 3) = x - 2 with no remainder.
A zero of a polynomial is a value of x that makes the polynomial equal to zero. For example, the polynomial x^2 - 5x + 6 has zeros at x = 2 and x = 3, because if we substitute these values into the polynomial, we get 0.
A solution of a polynomial equation is a value of x that satisfies the equation. For example, the polynomial equation x^2 - 5x + 6 = 0 has solutions at x = 2 and x = 3, because if we substitute these values into the equation, we get 0 = 0.
Finally, x-intercepts are the points where the graph of the polynomial intersects the x-axis. These are also known as zeros, because they are the values of x that make the polynomial equal to zero. For example, the polynomial x^2 - 5x + 6 has x-intercepts at x = 2 and x = 3, because these are the points where the graph of the polynomial intersects the x-axis.
In summary, factors, zeros, solutions, and x-intercepts are all different ways of describing the roots of a single polynomial equation. Factors and zeros are related to the factored form of the polynomial, while solutions and x-intercepts are related to the equation form and graph of the polynomial.