Objectives: Students will be able to…  Write a polynomial in factored form  Apply special factoring patterns 5.2: PART 1- FACTORING

1.What 2 numbers multiply together to get 24 and have a sum of 10? 2.What is the definition of a factor of a number? WARM UP:

 The process of breaking down a product into the quantities that multiply together to get the product  In essence, you are reversing the multiplication process  When factoring polynomials, you are breaking it up into simpler terms; breaking it into the terms that multiply together to get the polynomial FACTORING

 The largest factor that divides evenly into a quantity  In a polynomial, the GCF must be common to ALL terms.  Divide out the GCF (do not drop it!!!!!!!!!!!!!!) EXAMPLES: Factor GREATEST COMMON FACTOR (GCF)

x 2 + bx + c  When a = 1, EASY!!!!  Look for factor pairs of c that add up to b  Be aware of signs FACTORING TRINOMIALS

EXAMPLES: FACTOR

ax 2 + bx +c, where a ≠ y 2 + 5y n 2 -23n +7 FACTORING TRINOMIALS

3.5d 2 -14d p 2 -31p d 2 -17d+20 EXAMPLES, CONT.

 Always look for GCF first. If it has one, factor it out and try to factor what remains in parenthesis. DO NOT DROP GCF!!!!!!! EXAMPLES: Factor FACTORING COMPLETELY

 Difference between 2 perfect squares: a 2 – b 2 = (a + b) (a – b) For example: x 2 – 9 = (x + 3)(x – 3) 4x 2 – 25 = (2x + 5)(2x -5) SPECIAL FACTORING CASES

 Perfect Square Trinomials: a 2 + 2ab + b 2 = (a +b)(a +b) = (a+ b) 2 a 2 – 2ab + b 2 = (a –b) (a- b) = (a –b) 2 For example: x 2 + 8x + 16 = (x + 4)(x +4) = (x + 4) 2 x 2 - 8x + 16 = (x - 4)(x -4) = (x - 4) 2 SPECIAL FACTORING PATTERNS, CONT. Hint…How to recognize pattern: 1.The first & last terms are perfect squares 2.The middle term is twice the product of one factor from first term & one factor from last term.

1.n n q 2 – 12q t t p 2 – x 2 – x 2 EXAMPLES: FACTOR

1.5x k k y 3 – 24y 2 + 3y 4.x 2 + 5x x 2 – 4x r 3 – 48rs x x +42 FACTOR COMPLETELY, IF POSSIBLE