Question

name alyssa kennedy date 12-17-25 section 13.2
13.2 practice math modeling - factoring trinomials i ($x^2 + bx + c$)
find the integer pair that has the given product and sum. (ex. 1 on notes)
1.) product: 28 sum: 11 2.) product: -30 sum: -7
3.) product: -50 sum: 5 4.) product: 28 sum: -11

Explanation:

Problem 1: Product: 28, Sum: 11

Step1: List factor pairs of 28

Factor pairs of 28: (1, 28), (2, 14), (4, 7)

Step2: Check which pair sums to 11

1 + 28 = 29, 2 + 14 = 16, 4 + 7 = 11

Step1: List factor pairs of 30 (consider signs)

Factor pairs of 30: (1, 30), (2, 15), (3, 10), (5, 6). Since product is negative, one number is positive, one is negative.

Step2: Find pair with sum -7

Check pairs: (-10, 3): -10 + 3 = -7; product: -10 * 3 = -30

Step1: List factor pairs of 50 (consider signs)

Factor pairs of 50: (1, 50), (2, 25), (5, 10). Product is negative, so one positive, one negative.

Step2: Find pair with sum 5

Check pairs: (10, -5): 10 + (-5) = 5; product: 10 * (-5) = -50

Answer:

4 and 7

Problem 2: Product: -30, Sum: -7