Polynomials — Formula Sheet

Degree 1 → Linear Polynomial (e.g., 2x + 3)

A real number k is called a ZERO of polynomial p(x) if p(k) = 0.

To find if k is a zero, substitute x = k into the polynomial and check if the result is 0.

Example

For p(x) = x² - 3x - 4, p(-1) = (-1)² - 3(-1) - 4 = 1 + 3 - 4 = 0. So -1 is a zero.

The graph of y = ax + b (linear polynomial) is a STRAIGHT LINE that intersects the x-axis at exactly one point: (-b/a, 0). This x-coordinate is the zero.

The graph of y = ax² + bx + c (quadratic polynomial) is a PARABOLA.

For a quadratic polynomial p(x) = ax² + bx + c with zeroes α (alpha) and β (beta):

Sum of zeroes

α + β = -b/a = -(coefficient of x) / (coefficient of x²)

Product of zeroes

αβ = c/a = (constant term) / (coefficient of x²)

Polynomials are named based on their degree

Linear polynomials (degree 1) have the form ax + b, like 2x - 3 or √3x + 5.