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Algebra

Algebra. 10.5 Factoring Trinomials With a Lead Coefficient of 1 to Solve. Factoring to solve…. a quadratic expression can be solved by factoring and then using the zero-product property. Solve: x 2 + 10x + 21 = 0. …and whose sum is 10. Find two numbers whose product is 21.

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Algebra

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  1. Algebra 10.5 Factoring Trinomials With a Lead Coefficient of 1 to Solve

  2. Factoring to solve… • a quadratic expression can be solved by factoring and then using the zero-product property. Solve:x2 + 10x + 21 = 0 …and whose sum is 10. Find two numbers whose product is 21... (x + 7)(x + 3) = 0 x = -7 and -3 They should check!

  3. Figuring out the signs! Frame it with the signs. x2 + bx + c = 0 (x )(x ) = 0 + + Frame it with the signs. x2 – bx + c = 0 (x )(x ) = 0 - - Frame it with the signs. x2 – bx – c = 0 (x )(x ) = 0 - + The larger # goes here. Frame it with the signs. x2 + bx – c = 0 (x )(x ) = 0 - + The larger # goes here.

  4. Methods Method 1: List out all the factors of the constant in the trinomial. List factors of -36 6 and -6 -18 and 2 -12 and 3 Factor. x2 + 5x – 36 = 0 12 and -3 18 and -2 9 and -4 36 and -1 Frame it. (x )(x ) = 0 + 9 - 4 -9 and 4 -36 and 1 Which set of factors add to +5? Solve. x = 4 and -9 Method 2: Do this process in your head!!! Factor. x2 – 14x = -48 Put in standard form. x2 – 14x + 48 = 0 Frame it with signs. (x )(x ) = 0 - - 6 8 Solve. x = 6 and 8

  5. Solve. x2 – 15x – 7 = -61 + 61 +61 Put in standard form! x2 – 15x + 54 = 0 (x - )(x - ) = 0 9 6 x = 9 and 6

  6. Solve. 1) x2 + 3x – 18 = 0 x = 3 and -6 (x – 3)(x + 6) = 0 m2 + 11m + 10 = 0 2) m2 + 11m = -10 m = -10 and -1 (m + 10)(m + 1) = 0 x2 – 2x – 48 = 0 3) x2 – 2x – 40 = 8 x = -6 and 8 (x + 6)(x – 8) = 0 4) a2 – 33a = 280 a2 – 33a – 280 = 0 a = 40 and -7 (a – 40)(a + 7) = 0

  7. Solve. Then how do you solve the equation? 5) x2 + 3x = 6 x2 + 3x – 6 = 0 x = -3 - √33 x = -3 +√33 2 2 (x – )(x + ) = 0 If you think the quadratic equation cannot be factored, check the discriminant. If the discriminant is a perfect square: The equation can be factored. If the discriminant is not a perfect square: The equation cannot be factored. b2 – 4ac 32 – 4(1)(-6) 9 + 24 • Not a perfect square, • the trinomial cannot be factored.

  8. HW • P. 607-609 #15-47, 52-56

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