Math Problem Statement

Write two numbers that multiply to the value on top (-70) and add to the value on bottom (-3).

Solution

In the given problem, you are tasked with finding two numbers that:

  1. Multiply to give 70-70 (the number on top).
  2. Add up to 3-3 (the number on the bottom).

We need to find two numbers that satisfy both conditions. Let's factor 70-70 and then check which pair adds up to 3-3.

The factors of 70-70 are: (1,70),(1,70),(2,35),(2,35),(5,14),(5,14),(7,10),(7,10)(1, -70), (-1, 70), (2, -35), (-2, 35), (5, -14), (-5, 14), (7, -10), (-7, 10)

Now, we look for a pair whose sum is 3-3:

  • 7+(10)=37 + (-10) = -3

So, the two numbers are 7 and -10.

To summarize:

  • 7×(10)=707 \times (-10) = -70 (satisfies the multiplication condition)
  • 7+(10)=37 + (-10) = -3 (satisfies the addition condition)

The two numbers you're looking for are 7 and -10.

Would you like more details or have any questions? Here are 5 related questions:

  1. How do you find the factors of a negative number systematically?
  2. Can you apply this method to factor quadratics like x23x70x^2 - 3x - 70?
  3. What if the top number was positive—how would that change the process?
  4. What is the general rule for choosing signs in factor pairs?
  5. How do we factor when the numbers are not integers?

Tip: Always check both the product and sum conditions when factoring using this method to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Factoring
Algebra

Formulas

Multiplication and addition of integers

Theorems

Basic factoring principles for quadratic expressions

Suitable Grade Level

Grades 7-9