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Warm up

Warm up. Factor: 1. p 2 + 13p – 30 2. a 2 – 12a – 45 3. x 2 – 9x – 8. Lesson 5-9 Factoring Pattern for ax 2 + bx + c. Objective: To factor general quadratic trinomials with integral coefficients. Trial & Error Method. Example: 3x 2 + 2x - 8

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Warm up

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  1. Warm up • Factor: • 1. p2 + 13p – 30 • 2. a2 – 12a – 45 • 3. x2 – 9x – 8

  2. Lesson 5-9 Factoring Pattern for ax2 + bx + c Objective: To factor general quadratic trinomials with integral coefficients.

  3. Trial & Error Method • Example: 3x2 + 2x - 8 • List the factors of the a term and the c term. a = 3 factors: 1 and 3 c = -8 factors: 2 and 4 or 1 and 8 • Write down two sets of parentheses with empty spaces like this:( x    )( x    )

  4. Trial & Error Method 3x2 + 2x - 8 • Fill the spaces in front of the x's with a pair of possible factors of the a value. There is only one possibility for our example: (3x   )(1x   ) • Fill in the two spaces after the x's with a pair of factors for the constant. Let's say we choose (3x  8)(x  1).

  5. Trial & Error Method 3x2 + 2x - 8 • Decide what signs should be between the x's and the numbers. Here's a guide: If ax2 + bx + c then (x + h)(x + k) If ax2 - bx - c or ax2 + bx - c then (x - h)(x + k) If ax2 - bx + c then (x - h)(x – k)For our example 3x2 + 2x - 8 so (x - h)(x + k) (3x + 8)(x - 1)

  6. Trial & Error Method 3x2 + 2x - 8 • Test your choice by multiplying (use FOIL) the two parentheses together. • Swap out your choices if necessary. In our example, let's try 2 and 4 instead of 1 and 8: (3x + 2)(x - 4) • Reverse the order if necessary. Let's try moving the 2 and 4 around: (3x + 4)(x - 2)

  7. Trial & Error Method 3x2 + 2x - 8 • Double-check your signs if necessary. We're going to stick with the same order, but swap which one has the subtraction: (3x - 4)(x + 2) • This finally foils to the correct trinomial.

  8. Triple Play or “Magic” Method • Example: 4x2+ 5x + 1 • Multiply the a term (4 in the example) by the c term (1 in this example). • 4•1 = 4 • Find the two numbers whose product is this number (4) and whose sum is equal to the b term (5).1•4 = 41 + 4 = 5

  9. Triple Play or “Magic” Method • Take these two numbers (which we will call h and k) and substitute them into this expression:(ax + h)(ax + k)----------------------     a(4x + 4)(4x + 1)----------------------4

  10. Triple Play or “Magic” Method • Look to see which one of the two parenthesis terms in the numerator is evenly divisible by a {in this example it is (4x + 4)}. Divide this term by a and leave the other one as is.(4x + 4)(4x + 1)----------------------     8Answer:(x + 1)(4x + 1)

  11. Triple Play or “Magic” Method • Take the GCF (if any) out of either or both parentheses.(x + 1)(4x + 1)

  12. Try • 2b2 + 13b – 24 • 5y2 – 17y + 6 • 3k2 – 8k – 35

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