Polynomials. Polynomial a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 Where all exponents are whole numbers – Non negative integers.

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Polynomials

Polynomial a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 Where all exponents are whole numbers – Non negative integers

Polynomials a n x n + a n-1 x n-1 +….. + a 2 x 2 + a 1 x + a 0 a n is called the leading coefficient a 0 is called the constant term n is the degree of the polynomial

Polynomials are in standard form when the coefficients are in descending order Polynomial 7x 3 + 5x x Polynomial in standard form 5x 5 + 7x 3 + x + 2

Zero out terms Sometimes you need to represent all of the terms of a polynomial 5x 5 + 7x 3 + x + 2 5x 5 + 0x 4 + 7x 3 + 0x 2 + x + 2

Operations with polynomials Add – Combine like terms Multiply – Distribute each term of first polynomial into second

Add (7x 3 + 5x 2 + 3x + 1) + (3x 3 + 4x 2 - 2x + 5)

Subtract (4x 3 + 6x 2 + 2x + 6) - (4x 3 - 3x 2 + 5x + 9)

Multiply (4x 3 + 5x 2 + 2x + 7) (2x 3 - 3x 2 + 7x + 4)

Special products Difference of 2 squares (u + v) (u - v) u 2 - v 2 (5x + 7y) (5x – 7y) 25x 2 – 49y 2

Special products Square of a binomial (u + v) 2 u 2 + 2uv + v 2 (2x + 5y) 2 4x xy + 25y 2

Cube of a binomial (u + v) 3 u 3 + 3u 2 v + 3v 2 u + v 3 (2x + 3y) 3 8x 3 + 3(2x) 2 (3y) + 3(3y) 2 (2x) + 27y 3 8x x 2 3y + 27y 2 2x + 27y 3 8x x 2 y + 54y 2 x + 27y 3

Factoring Look for common factors among terms Look for special product patterns Try grouping 3 rd degree and splitting the middle on 2 nd degree polynomials