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Ch 8.5 (part 2) Factoring ax 2 + bx + c using the Grouping method

Ch 8.5 (part 2) Factoring ax 2 + bx + c using the Grouping method. Objective: To factor polynomials when a ≠ 1. Definitions. Polynomial in Standard Form : ax 2 + bx + c A polynomial written in descending order based on the exponents. Polynomial in Grouping Form : (ax + f 1 )(f 2 + c)

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Ch 8.5 (part 2) Factoring ax 2 + bx + c using the Grouping method

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  1. Ch 8.5 (part 2)Factoring ax2 + bx + cusing the Grouping method Objective: To factor polynomials when a ≠ 1

  2. Definitions Polynomial in Standard Form: ax2 + bx + c A polynomial written in descending order based on the exponents. Polynomial in Grouping Form: (ax + f1)(f2 + c) A polynomial written as the product of two (or more) binomials. Grouping: g(a + c) + h(a + c) = (g + h) + (a + c)

  3. Rules • Arrange the polynomial in Standard Form exponents in descending order • Place the b term at the top of the “x” • Place the ac term at the bottom of the “x” • Find the values that can be inserted into the left & right side of the “x” whose sum is on the top and product is on the bottom. use trial & error • Place those values into the Grouping Form • Factor each binomial • Group common factors add (+) bx f1x f2x ax2 multiply ()

  4. Example 1 2x2 + 5x + 3 add (+) 5x 2x 3x 6x2 multiply () (ax2 + ) (f2 + ) c f1 (2x2 + 2x) (3x + 3) +3(x + 1) factor each: 2x(x + 1) ( )( ) 2x + 3 x + 1 group:

  5. Example 2 2x2 − 9x + 7 add (+) -9x -2x -7x 14x2 multiply () (ax2 + ) (f2 + ) c f1 (2x2 − 2x) (−7x + 7) −7(x − 1) factor each: 2x(x − 1) ( )( ) 2x − 7 x − 1 group:

  6. Example 3 7x2 − 55x − 8 add (+) -55x x -56x -56x2 multiply () (ax2 + ) (f2 + ) c f1 (7x2 + x) (−56x − 8) −8(7x + 1) factor each: x(7x + 1) ( )( ) x − 8 7x + 1 group:

  7. Example 4 4x2 + 4x – 3 add (+) 4x -2x 6x -12x2 multiply () (ax2 + ) (f2 + ) c f1 (4x2 − 2x) (6x − 3) +3(2x − 1) factor each: 2x(2x − 1) ( )( ) 2x + 3 2x − 1 group:

  8. Classwork 1) 2) 2x2 + 7x + 3 2x2 − 19x + 24 (2x + 1)(x + 3) (2x − 3)(x − 8) 3) 4) 2x2 − 7x − 49 5x2 − 29x + 20 (5x − 4)(x − 5) (2x + 7)(x − 7)

  9. 5) 6) 4x2 + 4x + 1 4x2 + 0x − 25 (2x + 1)(2x + 1) (2x − 5)(2x + 5) 7) 8) 7x2 − 24x − 16 6x2 + 15x − 21 (7x + 4)(x − 4) (2x + 7)(3x − 3)

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