Problem Solving Involving Factoring

1. Problem Solving Involving
Factoring
Lorie Jane L. Letada
Module 2

2. At the end of this lesson, you are expected to:
 demonstrate understanding of the key
concepts of factors of polynomials; and
 solve problems involving factors of
polynomials.
Objectives

3. Let us recall the terms and the techniques we had in our
previous lesson.
Review

5. What’s New

6. Look at the picture. What would you feel when you are bombarded
with these problems?
How are you going to deal with these problems?
Below are suggested steps in solving problems.

7. What is it
Find two consecutive positive odd numbers such that the sum of
their squares is equal to 130.
In this lesson, you will need prior knowledge about factoring
polynomials and its techniques. Below are examples, please read and
analyze it carefully.
Example 1.

10. Example 2.
Seven times a certain integer is 5 more than twice its square.
Find the integer.
Represent:
Let x = integer
Equation:
7x = 2𝑥2
+ 5

12. Example 3.
The length of a rectangle is 5 cm more than its width. Find its length and
width when its area is 150 square cm.
Represent:
Let x = width of the rectangle
x + 5 = length of the rectangle
150 = area
Formula:
A = lw , where A is the area, l is the length
and w is the width
Equation:
(x + 5)(x) = 150

14. Activity 2.1
Directions: Read the problems carefully and answer using your
knowledge in factoring polynomials. Follow the steps suggested above
for you to be guided.
1. The square of a number equals nine times that
number. Find the number.
2. The product of two consecutive integers is
272. Find the value of each integer.

15. 3. The sum of a number and its square is 156. Find the
numbers.
4. Mario’s rectangular plot is 6 meters longer than
its width. The area of the plot is 16 square meters.
Find the length and the width of the plot.
5. Marilyn has a photograph which is 8 cm longer than
it is width and its area is 33 cm2. What are the
dimensions of the photograph?

16. What I need to remember
POINTS TO PONDER!
In solving problems involving factoring,
you may follow the following:
- UNDERSTAND
- REPRESENT
- EQUATION
- SOLUTION
- CHECK

17. “Be strong and of good
courage; do not be afraid, nor
be dismayed, for the LORD your
God is with you wherever you
go.”- Joshua 1:9