Question

question 7 of 10
use the table to identify the values of p and q that should be used to factor (x^2 + 9x - 10) as ((x + p)(x + q)).

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

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

Explanation:

Step1: Recall the factoring form

We know that \(x^{2}+bx + c=(x + p)(x + q)\), where \(b = p + q\) and \(c = p\times q\). For the quadratic \(x^{2}+9x - 10\), we need to find \(p\) and \(q\) such that \(p + q=9\) and \(p\times q=- 10\).

Step2: Analyze the table and options

Let's check each option:

• Option A: \(p=-1\), \(q = 10\). Then \(p + q=-1 + 10=9\) and \(p\times q=-1\times10=-10\). This satisfies both conditions.
• Option B: \(p = 1\), \(q=-10\). Then \(p + q=1-10=-9

eq9\). So this is incorrect.

• Option C: \(p = 2\), \(q=-5\). Then \(p + q=2-5=-3

eq9\). So this is incorrect.

• Option D: \(p=-2\), \(q = 5\). Then \(p + q=-2 + 5=3

eq9\). So this is incorrect.

Answer:

A. \(-1\) and \(10\)