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Today we will be focusing on factoring Trinomials when a is NOT equal to 1…..

Algebra 1 ~ Chapter 9.4 Factoring trinomials in form ax 2 + bx + c. Today we will be focusing on factoring Trinomials when a is NOT equal to 1…. First, always check to see if you can factor out a GCF first. If the answer is yes, do so. It will make the rest of the process MUCH easier .

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Today we will be focusing on factoring Trinomials when a is NOT equal to 1…..

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  1. Algebra 1 ~ Chapter 9.4 Factoring trinomials in form ax2 + bx + c Today we will be focusing on factoring Trinomials when a is NOT equal to 1…..

  2. First, always check to see if you can factor out a GCF first. If the answer is yes, do so. It will make the rest of the process MUCH easier. For example, factor 2x2 + 12x + 16 Before you jump to start trying to figure out the factors, do these 3 terms have a GCF other than 1? Yes they do, we can factor out 2… 2(x2 + 6x + 8) Now we have a trinomial where a = 1 and we know how to factor easily……… 2(x + 2)(x + 4)

  3. Example 1 – Factor 6x2 + 11x + 4 The way to factor trinomials like this is to factor by grouping…. *Want to split 11x into 2 terms so we can factor by grouping. The way we do this is to now find factors of a•cwhose sum still equals b. *Since 6•4 = 24, we need to find 2 #s that multiply together to = 24 and add up to 11 Make your table and try to find them. Now that we found the correct factors, rewrite 6x2 + 11x + 4as 6x2 + 3x + 8x + 4 and now factor by grouping: 3x(2x + 1) + 4(2x + 1) (3x + 4)(2x + 1)

  4. Example 2 - Factor the trinomial. Check your answer. 6x2 + 11x + 3 NO GCF!! The factors are (3x + 1)(2x + 3) Check: 6x2 + 9x + 2x + 3 6x2 + 11x + 3 

  5. Example 3 - Factor the trinomial. Check your answer. 10x2 + 12x – 16 2(5x2 + 6x - 8) GCF is 2 The factors are 2(5x - 4)(x + 2)

  6. Example 4 - You try one: Factor the trinomial. Check your answer. 3x2 - 16x + 16 NO GCF!! The factors are (3x - 4)(x - 4) Check: 3x2 - 12x - 4x + 16 3x2– 16x + 16 

  7. “Quiz” Factor each trinomial. Check your answer. 1. 5x2 + 17x + 6 2. 6x2 – 23x + 7 3. 6x2- 21x + 9 4. 5x2+ 27x + 10 = 0 (5x + 2)(x + 3) (3x– 1)(2x– 7) 3(2x– 1)(x– 3) x = -5 or x = -2/5

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