P.3 Polynomials and Special Products Unit P:Prerequisites for Algebra 5-Trig

Definition of a Polynomial in x Let a 0, a 1, a 2, …, a n be real numbers and let n be a nonnegative integer. A polynomial in x is an expression of the form a n x n + a n-1 x n-1 + … + a 1 x + a 0 where a n ≠ 0. The polynomial is of degree n, an is the leading coefficient, and a 0 is the constant term.

Standard Form In standard form, a polynomial is written in descending powers of x.

Operations with Polynominials You can add and subtract polynomials by combining like terms. To find the product you must distribute.

Special Products Sum and Difference of Same Terms (a + b)(a – b) = a 2 – b 2 Square of a Binomial (a + b) 2 = a 2 + 2ab + b 2 (a – b) 2 = a 2 – 2ab + b 2 Cube of a Binomial (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (a – b) 3 = a 3 – 3a 2 b + 3ab 2 – b 3

Application