Factoring Factoring in the format ax2+bx+c Problem 1 X 2 + 7x + 10.

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Factoring Factoring in the format ax2+bx+c

Problem 1 X 2 + 7x + 10

Example 1 Factor ax 2 + bx + c A. Factor 5x x In this trinomial, a = 5, b = 27, and c = 10. You need to find two numbers with a sum of 27 and with a product of 5 ● 10 or 50. Make an organized list of the factors of 50 and look for the pair of factors with the sum of 27. 1, , 2527 The correct factors are 2 and 25. Factors of 50 Sum of Factors 5x x + 10 = 5x 2 + mx + px + 10Write the pattern. = 5x 2 + 2x + 25x + 10m = 2 and p = 25

Example 1 = (5x 2 + 2x) + (25x + 10)Group terms with common factors. = (x + 5)(5x + 2)Distributive Property = x(5x + 2) + 5(5x + 2)Factor the GCF. Answer: (x + 5)(5x + 2) or (5x + 2)(x + 5)

Example 1 Factor ax 2 + bx + c B. Factor 4x x The GCF of the terms 4x 2, 24x, and 32 is 4. Factor this term first. 4x x + 32 = 4(x 2 + 6x + 8)Distributive Property Now factor x 2 + 6x + 8. Since the lead coefficient is 1, find the two factors of 8 whose sum is 6. 1, 89 2, 46The correct factors are 2 and 4. Factors of 8 Sum of Factors

Example 1 A.(3x + 7)(x + 5) B.(3x + 1)(x + 35) C.(3x + 5)(x + 7) D.(x + 1)(3x + 7) A. Factor 3x x + 35.

Example 3 A.(3x + 1)(x – 3) B.(3x – 3)(x – 1) C.(3x – 1)(x – 3) D. prime Factor 3x 2 – 5x + 3, if possible.

2x 2 + 7x + 6

2x x + 18

3x x + 8

2x 2 - 9x + 7

4x x - 21

3x 2 + 4x + 1