Algebraic Expressions And Polynomials — Formula Sheet

General form of a polynomial in one variable x: a_0 + a_1x + a_2x^2 + ... + a_nx^n

2x + 3x = (2+3) × x = 5x

9x^2y^2 - 5x^2y^2 = (9-5)x^2y^2 = 4x^2y^2

Degree of a term = sum of the exponents of the variables in that term

Degree of a polynomial = degree of the term having highest degree and non-zero coefficient

Degree of a non-zero constant: 3 = 3 × x^0

Arithmetical numbers are like terms because 3 = 3x^0 and -5 = -5x^0.

x = 1 is a zero of 5x^3 + 3x^2 - 4x - 4 because substitution gives 0.

x = -1 is not a zero of x^3 + 3x^2 + 3x + 2 because the value is 1, not 0.