Question

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


p +
q
q
1
-10
-9
-1
10
9
2
-5
-3
-2
5
3
02 and -5
• -1 and 10
O -2 and 5
• 1 and -10

Answer 1

To factor the quadratic expression \(x^2 + 3x - 10\) in the form \((x + p)(x + q)\), we need to find two numbers \(p\) and \(q\) such that:

1. \(p + q = 3\) (the coefficient of \(x\))
2. \(p \cdot q = -10\) (the constant term)

Let's evaluate the pairs of values from the options listed in the table:

1. **1 and -10:**
\(p + q = 1 - 10 = -9\) (not a match)

2. **-1 and 10:**
\(p + q = -1 + 10 = 9\) (not a match)

3. **-2 and 5:**
\(p + q = -2 + 5 = 3\) (match for the sum)
\(p \cdot q = -2 \cdot 5 = -10\) (match for the product)

4. **2 and -5:**
\(p + q = 2 - 5 = -3\) (not a match)

Thus, the correct values for \(p\) and \(q\) are **-2 and 5**.

Therefore, the factorization of \(x^2 + 3x - 10\) is \((x - 2)(x + 5)\).