Factor It’s a big deal!.

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Presentation transcript:

Factor It’s a big deal!

Any amount of terms #1 GCF Always look for and pull out the Greatest Common Factor if the polynomial has one.

1. 6x² + 4x – 8 Ans: 2(3x²+2x -4) 2. 25x³ - 5x² - 10x GCF 1. 6x² + 4x – 8 Ans: 2(3x²+2x -4) 2. 25x³ - 5x² - 10x Ans: 5x(5x²- x- 2)

Just two terms Difference of squares a² - b² = (a + b)(a – b)

1. x² -16 Ans: (x + 4)(x – 4) 2. 4x² - 25 Ans: (2x – 5)(2x + 5) Difference of squares 1. x² -16 Ans: (x + 4)(x – 4) 2. 4x² - 25 Ans: (2x – 5)(2x + 5)

Just Two terms Sum or Difference of cubes a³ + b³ = (a + b)(a² - ab + b²) a³ - b³ = (a – b)(a² + ab + b²)

Cubes 1. x³-y³ Ans: (x-y)(x² + xy + y² 2. 8a³+ 1 Ans: (2a + 1)(4a² - 2a + 1) 3. m³ -27 Ans: (m – 3)(m² + 3m + 9)

Three Terms Trinomial lead coefficient of one x² + ax + b = ( x + ___)(x + ___) what times what = last term what plus what = middle term

1. x² + 8x + 12 Ans: (x + 6)(x + 2) 2. x² -7x + 12 Ans: (x- 4)(x – 3) Trinomial Lead Coef. 1 1. x² + 8x + 12 Ans: (x + 6)(x + 2) 2. x² -7x + 12 Ans: (x- 4)(x – 3)

Trinomial lead coefficient not one ax² + bx + c Guess and check 3 Terms Trinomial lead coefficient not one ax² + bx + c Guess and check

Trinomial Lead Coef. Not 1 1. 2x² + 7x + 3 Ans: (2x +1)(x + 3) 2. 3x² + 8x + 4 Ans: (3x + 2)(x + 2)

4 or more terms Grouping Group pairs or groups, and pull out a common factor. Write down what the groups have in common, times what’s left over from left to right.

1. xa – 2x + 6a – 12 Ans: (x + 6)(a – 2) 2. xm – 2x -6m + 12 Grouping 1. xa – 2x + 6a – 12 Ans: (x + 6)(a – 2) 2. xm – 2x -6m + 12 Ans: (x – 6)(m - 2)

Homework Page 242-243:16-44 even