Polynomials — Chapter Summary

Linear polynomial (degree 1)

Linear polynomial (degree 1): ax + b, where a ≠ 0. Example: 2x - 3. Quadratic polynomial (degree 2): ax² + bx + c, where a ≠ 0. Example: 3x² - 5x + 2.

A real number k is

A real number k is a zero of polynomial p(x) if p(k) = 0. For example, if p(x) = x² - 3x - 4, then p(4) = 16 - 12 - 4 = 0, so 4 is a zero. Step-by-ste

Zeroes of a polynomial are

Zeroes of a polynomial are the x-coordinates where the graph intersects the x-axis. Linear polynomial: exactly 1 zero (straight line crosses x-axis on

For quadratic polynomial ax² + bx

For quadratic polynomial ax² + bx + c with zeroes α and β: Sum of zeroes: α + β = -b/a. Product of zeroes: αβ = c/a. Step-by-step verification example

For cubic polynomial ax³ + bx²

For cubic polynomial ax³ + bx² + cx + d with zeroes α, β, γ: Sum of zeroes: α + β + γ = -b/a. Sum of products taken two at a time: αβ + βγ + γα = c/a.