Question

juanita begins to factor an expression as shown.
$x^2 + 3x - 18 = (x + square)(x - square)$
what numbers should be placed in the boxes from left to right?

• 3 and 6
• 2 and 9
• 6 and 3
• 9 and 2

Explanation:

Step1: Recall factoring quadratic

For \(x^2 + bx + c=(x + m)(x + n)\), \(m + n = b\), \(m\times n=c\). Here, \(c=-18\), so one factor is positive, one negative. Let the factors be \(p\) (positive) and \(-q\) (negative), so \((x + p)(x - q)=x^2+(p - q)x - pq\). We need \(p - q = 3\) and \(pq = 18\).

Step2: Solve for p and q

Find two numbers \(p,q\) such that \(pq = 18\) and \(p - q = 3\). Test pairs: \(6\) and \(3\): \(6\times3 = 18\), \(6 - 3 = 3\). So \(p = 6\), \(q = 3\). Thus, \((x + 6)(x - 3)\).

Answer:

6 and 3 (the option "6 and 3")