What are Polynomials?

A polynomial is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

• Term: Standard part of a polynomial.
• Coefficient: Number multiplied by the variable.
• Degree: The highest power of the variable in the polynomial.

Graphing Polynomials

The zeroes of a polynomial p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the x-axis.

• Linear Polynomial: Crosses x-axis at exactly 1 point.
• Quadratic Polynomial: Crosses x-axis at 0, 1, or 2 points (Parabola).
• Cubic Polynomial: Crosses x-axis at up to 3 points.

Quadratic Polynomials (ax² + bx + c)

If α and β are the zeroes, then:

• Sum of Zeroes (α + β): -b/a
• Product of Zeroes (αβ): c/a

Cubic Polynomials (ax³ + bx² + cx + d)

• α + β + γ = -b/a
• αβ + βγ + γα = c/a
• αβγ = -d/a