Question

question 2 of 10
use the table to identify the values of p and q that should be used to factor (x^2 + 3x - 10) as ((x + p)(x + q)).

p	q	p+q
-1	10	9
2	-5	-3
-2	5	3

a. -1 and 10
b. 2 and -5
c. -2 and 5
d. 1 and -10

Explanation:

Step1: Recall factoring form

For a quadratic \(x^2 + bx + c\), factoring as \((x + p)(x + q)\) means \(p + q = b\) and \(p \times q = c\). Here, \(b = 3\) and \(c = -10\).

Step2: Check table for \(p + q = 3\)

Looking at the table, the row where \(p + q = 3\) has \(p=-2\) and \(q = 5\) (since \(-2 + 5 = 3\)). Also, \(p \times q=-2\times5=-10\), which matches \(c\).

Answer:

C. \(-2\) and \(5\)