Roots/Graphs of Polynomials

The roots of a polynomial are the values of x for which the polynomial equals zero. They are also known as zeros or x-intercepts.

Set each factor equal to zero: -x = 0 (x = 0), (x + 1) = 0 (x = -1), (x - 3) = 0 (x = 3). The roots are x = 0, -1, 3.

When a graph crosses the x-axis, it indicates that the polynomial has a root at that point, meaning the value of the polynomial is zero.

End behavior describes how the values of f(x) behave as x approaches positive or negative infinity.

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches +∞.

As x approaches -∞, f(x) approaches +∞; as x approaches +∞, f(x) approaches -∞.

The x-intercepts (or roots) indicate the values of x where the polynomial equals zero, which are critical for graphing the function.

Each root of a polynomial corresponds to a factor of the polynomial set equal to zero.

The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n roots in the complex number system, counting multiplicities.

You can determine the number of real roots by analyzing the graph of the polynomial or using the discriminant for quadratic polynomials.