Math8_Q1_Wk2_D1-4_PPT.pptx

Department of Education
Schools Division of NEGROS ORIENTAL
MATHEMATICS
MATHEMATICS
Competency:
Solves problems involving
factors of polynomials
(M8AL-Ib-2)
Quarter 1 Week 2
Prepared by:
Sharon C. Grio & Carla A. Araneta
Balugo NHS

MATHEMATICS
MATHEMATICS
LEARNING OBJECTIVES:
Knowledge: Recognizes the concepts
involving factors of polynomials
Skills: Solves problems involving
factors of polynomials.
Attitude: Develops patience in solving
problems involving factors of polynomials.

MATHEMATICS
MATHEMATICS
Solving Problems Involving
Factors of Polynomials

MATHEMATICS
MATHEMATICS
LEARNING RESOURCES
Teacher’s Guide (TG) in Math 8, pp. 49 – 53
Learner’s Module (LM)in Math 8, pp. 49 -58.
Elementary Algebra I. 2000. pp. 212-216*
Self-Learning Kit in Math 8 Problems
Involving Factors of Polynomials (Q1W2) pp.
1-15.
www.jonblakely.com/wpcontent/uploads/4_8v2.pdf

MATHEMATICS
MATHEMATICS
DRILL:
Factor the following :
1. n2 - p2
2. x2 + 4x + 4
3. x2 + 5x + 6
(n+p) (n-p)
(x+2)2
(x+3)(x+2)

MATHEMATICS
MATHEMATICS
Unlocking of difficult terms:
• Polynomial
• Area
• Factor
• Perimeter
• Product

MATHEMATICS
MATHEMATICS
POLYNOMIAL
Is a finite sum of terms each of
which is a real number or the product
of a numerical factor and one or
more variable factor raised to a
whole – number powers.

MATHEMATICS
MATHEMATICS
AREA
The amount of surface contained by
a figure.
FACTOR
An exact divisor of a number.

MATHEMATICS
MATHEMATICS
PERIMETER
The distance around a polygon.
PRODUCT
The answer of multiplication

MATHEMATICS
MATHEMATICS
Steps in solving word problems:
•First: Interpret and know the problem
carefully.
•Second: Replace the mathematical words to
symbols and use variables for representations.
•Third: Make an equation.
•Fourth: Solve algebraically.
• Fifth: State your complete answer.

MATHEMATICS
MATHEMATICS
Group Activity
1. The length of a rectangular garden is
2x – 3 meters and its width is x - 1 meters.
What is the total area of the rectangular
garden?
2. The area of square garden is x2 – 14x + 49,
find its dimension.

MATHEMATICS
MATHEMATICS
Answers
1. Solution:
Length (l) = 2x – 3; Width (w) = x – 1

MATHEMATICS
MATHEMATICS
2. Solution: Area of a Square = s2
s2 = Area of a Square
:The garden has
side of x – 7
meters in order to
have an area of
x2 - 14x + 49.
Therefore its
dimension is x – 7
meters by x – 7
meters

MATHEMATICS
MATHEMATICS
PRACTICE # 1
Solve the following below.
1. What is the area of a square garden if
it has a side of 2x – 5 meters?
2. The area of a rectangular field is
x2 +x – 6 meters and its length is
x – 2 meters. How long is its width?

MATHEMATICS
MATHEMATICS
SOLUTION & ANSWER
1. Solution:
Area of Square = s2
 
  
25
20
4
5
2
5
2
5
2
2
2








x
x
x
x
x

MATHEMATICS
MATHEMATICS
2. Solution: Find the width(w)
Area of a Rectangle = l x w
The width of a rectangular field of x2 +x – 6 meters is x+3.

MATHEMATICS
MATHEMATICS
PRACTICE # 2
Solve the following below.
1.What is the area of a square garden if it has
a side of 3a + 6 meters?
2.The area of a rectangular field is
x2 + 14x + 49 meters and its length is x +7
meters. How long is its width?
(9a2 + 36a + 36)
(x + 7)

MATHEMATICS
MATHEMATICS
Group 1 & 4: Problem #1 (Rap/Sing)
Group 2 & 5: Problem #2 (Declamation – 1 rep.)
Group 3 & 6: Problem #3 (Speech Choir)

MATHEMATICS
MATHEMATICS
(Rap/Sing)
What is the area of a square garden if it has a side of 3x +
5 meters?
(Declamation)
The area of a rectangular field is x2 +3x + 2 meters and its
length is x +1 meters. How long is its width?
(Speech Choir)
The length and width of a rectangular rice field is 7x – 8
meters and 7x + 8 meters respectively. What is its area?

MATHEMATICS
MATHEMATICS
(Presentation of each group)
Guide Question:
1. From your answers, do they have similarities /
differences?
2. Which group answered their problem correctly?
3. Is there any group who didn’t get the correct answer?
Why?

MATHEMATICS
MATHEMATICS
Choose the letter of the correct answer. Show your
solution on how you got that answer (10 points)
The area of a square is 16 square meters. Find the
length of one side.
a. -4 c. 8
b. 4 d. 16

MATHEMATICS
MATHEMATICS
Your classmate factored x2 + 36 using
difference of two squares. How will you make
him realize that his answer is not correct?

MATHEMATICS
MATHEMATICS
How special product is applied to real life
problems?
Special product and factoring techniques are important
tools for solving real life problems such as finding the
dimension of an enclosed field or box, sharing a cost,
finding average speed or average time covered, and
solving mixture or work problems.

MATHEMATICS
MATHEMATICS
Is it important to you as a student? In what
particular way?
In solving problems involving factors of polynomials, it
must be solved algebraically. It needs time and great
patience so that you will be able to value the
contributions to life such as finding the dimension of an
enclosed field or box, sharing a cost, finding average
speed or average time covered, and solving mixture or
work problems.

MATHEMATICS
MATHEMATICS
What concepts have you learned from
factoring that can be applied in your daily
living?
Factoring is a useful skill in real life. Common
application include , dividing something into equal
pieces, exchanging money, comparing prices,
understanding time and making conclusions during
travel.

MATHEMATICS
MATHEMATICS
What are the suggested steps in solving word
problems?
a. Interpret and know the problem carefully.
b. Replace the mathematical words to symbols and use variables for
representation.
c. Make an equation.
d. Solve algebraically.
e. State your complete answer.

MATHEMATICS
MATHEMATICS
Problem Solving. (Individual Output)
Solve each problem and show your solution. (10 points each)
1. The length of a triangle is three times the
width. If the area of a rectangle is 432 m2, find
the length and width.

MATHEMATICS
MATHEMATICS
2. The product of two consecutive integers is
210. Find all such pairs of integers.

MATHEMATICS
MATHEMATICS
3. The square of a number increases by five
times the number is 14. Find the number.

MATHEMATICS
MATHEMATICS
4. The area of a rectangle door is given by the
trinomial x2 - 14x + 45. The door’s width is
(x - 9). What is the door’s length?

MATHEMATICS
MATHEMATICS
5. The area of a rectangle is x2 - 6x -16. If the
width is x + 2, then what is the length?

MATHEMATICS
MATHEMATICS
1. The length of a triangle is three times the width. If the area of a rectangle is 432
m2, find the length and width.
2. The product of two consecutive integers is 210. Find all such pairs of integers.
3. The square of a number increases by five times the number is 14. Find the
number.
4. The area of a rectangle door is given by the trinomial x2 -14x +45. The door’s
width is (x-9). What is the door’s length?
5. The area of a rectangle is x2 -6x-16. If the width is x+2, then what is the length?

MATHEMATICS
MATHEMATICS
KEY ANSWER
1. 3x(x) = 432; W=12 m, L = 36m
2. x(x+1) = 210; (-15 & 14)
3. x2 +5x =14; (2, -7)
4. (x- 5)
5. (x-8)

MATHEMATICS
MATHEMATICS
Choose the letter that best corresponds in each
item. Write your answer in a separate sheet of
paper.

MATHEMATICS
MATHEMATICS
1. If a square pool is to be made a rectangle such that
the length is increased by 6 units and the width is
decreased by 6 units, what will happen to its area?
a. The area will increase by 12
b. The area will decrease by 12
c. The area will increase by 36.
d. The area will decrease by 36

MATHEMATICS
MATHEMATICS
2. The area of a rectangular garden is
(12x2 – 8x – 15)m2, what are its dimensions?
a. (3x – 5)m by (4x + 3)m
b. (6x + 5)m by (2x – 3)m
c. (6x – 3)m by (2x – 5)m
d. (12x – 15)m by (x + 1)

MATHEMATICS
MATHEMATICS
3. How much wood is needed in the window
frame illustrated below?
a. (m + e)2 square units
b. (m2 + e2) square units
c. (m – e)(m – e) square units
d. (m + e)(m – e) square units

MATHEMATICS
MATHEMATICS
4. If the area of a square garden is (4x2 – 12x +
9) square units, is it possible to solve its sides?
a. Yes, using factoring difference of two squares.
b. No, one of the sides must be given
c. Yes, the area is a perfect square trinomial
d. No, the area is not factorable

MATHEMATICS
MATHEMATICS
5. Liza factored the expression 15x2y3 + 10x4y + 5xy as
5xy (3xy2 + 2x3). Did Liza factor it correctly?
a. No, because 5xy is not the common factor.
b. Yes, because the last term is cancelled out
c. Yes, there exist a common factor on all terms
d. No, because the last term when factored is 1 and
should not be omitted expression is (x + 3)(x – 3)

MATHEMATICS
MATHEMATICS
Prepared by:
SHARON C. GRIO CARLAA. ARANETA
Balugo NHS Balugo NHS
Checked by:
ROLAND P. OJARIO MARCELA O. CATALBAS
Math Coordinator – JHS Math Coordinator – SHS
District QA Team District QA Team
ANTONIETAA. MERCED
PNSHS – TIC
Chairperson, District QA Team

Math8_Q1_Wk2_D1-4_PPT.pptx

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