Polynomials — Formula Sheet

A polynomial in x is an algebraic expression containing the sum of a finite number of terms of the form ax^n, where a is a real number, a ≠ 0, and n i

General polynomial of degree n: p(x) = a_0x^n + a_1x^(n-1) + a_2x^(n-2) + ... + a_(n-1)x + a_n

p(k) means the value of the polynomial p(x) when x is replaced by k.

a real number k is said to be a zero of a polynomial p(x), if p(k) = 0.

Zero of a linear polynomial: k = -b/a

The graph of y = ax + b intersects the X-axis at exactly one point (-b/a, 0).

A quadratic polynomial can have either two distinct zeroes or two equal zeroes (one zero), or no zeroes.

A polynomial of degree n has at most n zeroes.

For ax^2 + bx + c, a ≠ 0: α + β = -b/a ; αβ = c/a

For p(x) = x^2 - 2x - 3, the values at x = 3 and x = -1 are 0, so 3 and -1 are zeroes.