Lesson 9-3 Factoring Trinomials: x 2 + bx + c

Definitions Factoring - To factor quadratic trinomials of the form x 2 + bx + c, find two integers, m and n, whose sum is equal to b and whose product is equal to c. Then write x 2 + bx + c using the pattern (x + m)(x + n). Symbol: x 2 + bx + c = (x + m)(x + n) when m + n = b and mn = c. Example: x 2 + 5x + 6 = (x + 2)(x + 3), since = 5, and 2  3 = 6.

Finding factors when… b and c are positive, both factors are positive. Factor x 2 + 6x + 8 Factors of 8 Sum of Factors 1,8 2,4 9 6

Factor x 2 + 7x + 12

Finding factors when… b is negative and c is positive, both factors are negative Factor x x + 16 Factors of 16 Sum of Factors -1, , , -4-8

Factor x x + 27

Finding factors when… b is negative and c is negative, the largest of the two factors is negative. Factor x 2 + x - 12 Factors of -12 Sum of Factors 1, , , , 6 3, -4 -3, 4 4 1

Factor x 2 + 3x - 18

Finding factors when… b is positive and c is negative, the largest of the two factors is positive. Factors of -18 Sum of Factors 1, , , -9-7 Factor x 2 -7x - 18

Factor x 2 - x - 20

Solve an Equation by Factoring Solve x 2 + 5x = 6 x 2 + 5x = 6 x 2 + 5x - 6 = 0 (x - 1)(x + 6) = 0 x - 1 = 0 or x + 6 = 0 x = 1 x = -6 Solution set is {1,-6}

Solve x 2 + 2x = 15

Solve Marion has a small art studio in her back yard. She wants to build a new studio that has three times the area of the old studio by increasing the length and width by the same amount. What are the dimensions of the new studio? Existing Studio 12 ft 10 ft x x