Graphs of Polynomials

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, $$2x^2 + 3x + 1$$ is a polynomial.

The zeros of a polynomial are the values of x that make the polynomial equal to zero. They are also known as the roots of the polynomial.

Set the polynomial equal to zero: $$x(x - 8) = 0$$ . The solutions are $$x = 0$$ and $$x = 8$$ .

A polynomial has a zero at the origin if substituting $$x = 0$$ into the polynomial results in a value of zero.

The degree of a polynomial is the highest power of the variable in the polynomial. For example, in $$2x^3 + 3x^2 + 1$$ , the degree is 3.

A factor of a polynomial is a polynomial that divides the original polynomial without leaving a remainder. For example, $$(x - 1)$$ is a factor of $$x^2 - 1$$ .

To determine if a number is a zero of a polynomial, substitute the number into the polynomial. If the result is zero, then it is a zero.

If $$r$$ is a zero of a polynomial $$f(x)$$ , then $$(x - r)$$ is a factor of $$f(x)$$ .

The polynomial function can be expressed as $$h(x) = x(x - 8)$$ .

The zeros are $$x = 1$$ and $$x = -3$$ .