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Factoring x 2 + bx + c

Factoring x 2 + bx + c. Section 9.5. Main Idea. x 2 + bx + c = (x + p)(x + q) where p + q = b and pq = c. I see SIGNS…. In the trinomial x 2 + bx + c. This tells me what sign that is. + Tells me my factors will have the same sign. So if I had the polynomial x 2 - bx + c

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Factoring x 2 + bx + c

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  1. Factoring x2 + bx + c Section 9.5

  2. Main Idea x2 + bx + c = (x + p)(x + q) where p + q = b and pq = c

  3. I see SIGNS… • In the trinomial x2 + bx + c This tells me what sign that is + Tells me my factors will have the same sign. So if I had the polynomial x2 - bx + c My factors would be (x - ___ ) (x - ___ )

  4. Example • Factor x2 + 11x + 18 (x + ___ ) (x + ___ ) I am looking for two numbers that add to 11 and multiply to 18… So, (x + 9) (x + 2)

  5. Another Example • Factor n2 – 6n + 8 (x + ___ ) (x + ___ ) I am looking for two numbers that add to -6 and multiply to 8… (x - 2) (x - 4)

  6. A Different sign… • Factor y2 + 2y - 15 (-) Says my factors have different signs But they still have to add to 2 and multiply to -15

  7. Example Factor y2 + 2y – 15 This is it! So, my factors are (x-3) (x+5)

  8. Solving Equations To solve a polynomial equation • First find the factors • Second apply zero product principle

  9. Example • Solve x2 +5x = 50 x2 + 5x – 50 = 0 Make equation equal 0 Next, Factor into (x-10)(x+5) = 0 Zero product principle says x-10 = 0 or x + 5 = 0 Therefore x = 10, or -5

  10. Finding the zeros of a function • f(x) = x2 + 10x – 39 This means to factor and solve the equation set to zero. (x-13) (x + 3) = 0  x = 13 or -3

  11. TRY IT!! • Factor • x2 – 4x + 3 • t2 – 17t – 60 • x2 + 4x - 32 • t2 + 9t + 14 • e) a2 + 6a - 72 Try these…Ask questions and make sure you can do these. Turn these in today! Homework 9.5, 3-17 odd, 20-28 even, 31-41 odd

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