Question

for the two numbers listed, find two factors of the first number such that their product is the first number and their sum is the second number.

\\-12, -1\\

Explanation:

Identify the given values and target

We are given two numbers:
First number (product): \(-12\)
Second number (sum): \(-1\)

We need to find two integers, let's call them \(a\) and \(b\), such that:

$$ a \cdot b = -12 $$

$$ a + b = -1 $$

List factor pairs of the product

Since the product is negative (\(-12\)), the two factors must have opposite signs (one positive and one negative).
Let's list the factor pairs of \(-12\) and calculate their sums:

• \(1\) and \(-12\) \(

ightarrow 1 + (-12) = -11\)

• \(-1\) and \(12\) \(

ightarrow -1 + 12 = 11\)

• \(2\) and \(-6\) \(

ightarrow 2 + (-6) = -4\)

• \(-2\) and \(6\) \(

ightarrow -2 + 6 = 4\)

• \(3\) and \(-4\) \(

ightarrow 3 + (-4) = -1\)

• \(-3\) and \(4\) \(

ightarrow -3 + 4 = 1\)

Select the correct pair

We look for the pair whose sum is exactly \(-1\).
From our list, the pair \(3\) and \(-4\) satisfies this condition:

$$ 3 \cdot (-4) = -12 $$

$$ 3 + (-4) = -1 $$

Thus, the two factors are \(3\) and \(-4\).

Answer:

3, -4