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P.3A Polynomials and Special Factoring In the following polynomial, what is the degree and leading coefficient? 4x 2 - 5x 7 - 2 + 3x Degree = Leading coef. = 7 -5 Ex. 1 Adding polynomials (7x 4 - x 2 - 4x + 2) - (3x 4 - 4x 2 + 3x)First, dist. the neg. = 4x 4 + 3x 2 - 7x + 2

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Ex. 2Foil (3x - 2)(5x + 7)= 15x 2 + 21x - 10x - 14 = 15x 2 + 11x - 14 Special Products Sum and Difference (x + y)(x – y) = x 2 – y 2 Square of binomial (x + y) 2 = x 2 + 2xy + y 2 (x – y) 2 = x 2 – 2xy + y 2 Cube of Binomial (x + y) 3 = x 3 + 3x 2 y + 3xy 2 + y 3 (x − y) 3 = x 3 − 3x 2 y + 3xy 2 − y 3

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Ex. 3Sum and difference (5x − 9)(5x + 9) = 25x 2 − 81 Ex. 4Square of Binomial (6x − 5) 2 = 36x 2 − 60x + 25 Ex. 6The product of Two Trinomials (x + y - 2)(x + y + 2) =x 2 + xy + 2x + xy + y 2 + 2y -2x - 2y - 4 = x 2 + 2xy + y 2 - 4

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