 # 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.

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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 + Tells me my factors will have the same sign. This tells me what sign that is So if I had the polynomial x 2 - bx + c My factors would be (x - ___ ) (x - ___ )

Example Factor x 2 + 11x + 18 (x + ___ ) I am looking for two numbers that add to 11 and multiply to 18… Factors Sum 1, 18 19 2, 9 11 3, 6 9 So, (x + 9) (x + 2)

Another Example Factor n 2 – 6n + 8 (x + ___ ) I am looking for two numbers that add to -6 and multiply to 8… Factors Sum -1, -8 -9 -2, -4-6 (x - 2) (x - 4)

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

Example Factor y 2 + 2y – 15 Factors (-15)Sum (2) -1, 1514 1, -15-14 3, -5-2 -3, 52 This is it! So, my factors are (x-3) (x+5)

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

Example Solve x 2 +5x = 50 x 2 + 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

Finding the zeros of a function f(x) = x 2 + 10x – 39 This means to factor and solve the equation set to zero. (x-13) (x + 3) = 0  x = 13 or -3

TRY IT!! Factor a)x 2 – 4x + 3 b)t 2 – 17t – 60 c)x 2 + 4x - 32 d)t 2 + 9t + 14 e) a 2 + 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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