Strategic Intervention Material (SIM) was provided for Grade 10 students to enhance learning and to motivate and stir up the attention and interest of the students until they master the topic. This material depicts the entire definition of learning since it concludes a systematic development of students’ comprehension on a distinct lesson in Mathematics 10.

1. or
Department of Education
Region III
Schools Division of Zambales
District of Masinloc
TALTAL NATIONAL HIGH SCHOOL
Masinloc, Zambales
STRATEGIC INTERVENTION MATERIAL (SIM)
(FACTORS OF POLYNOMIAL)
IN
GRADE 10 MATHEMATICS
Prepared by:
ROCHELLE E. OLIVA
Teacher I

2. HOW TO PLAY
This is a FACT-OR-BLUFF game played in five rounds. During each round, players
will solve a given problem. There should be one person who will stand as the
“MASTER BLUFFER or the MOTHER FACTer”. He/she will tell whether the
answer of the players is a fact or a bluff.
3. Create a scorecard.
4. During rounds 1 and 2, players will
2. Have a deal with other players. Set the consequence which will be given to the
loser/s.
ROUND
1
ROUND
2
ROUND
3
ROUND
4
ROUND
5
TOTAL
SCORE
5. The person/s with the highest score and make it to play until round 5 will win.
TIP:
THERE’S REALLY NO SPECIAL STRATEGY INVOLVED. IT’S ALL ABOUT
YOUR UNDERSTANDING AND DETERMINATION TO WIN. THESE MAKE
THIS GAME FUN AND EXCITING. ENJOY!
1. Choose the “MASTER BLUFFER/MOTHER FACTer”.
NOTE: THE CONSEQUENCE SHOULD NOT HARM THE LOSER/S.
THIS IS A FRIENDLY GAME. OTHERWISE, YOU’LL BE GIVEN A
SANCTION.
get 1 pt. for each correct answer. Those players who will score 5pts. or below in the first
two rounds will be eliminated. In rounds 3 and 4, two points will be given for each correct
answer. Those players who will score 10pts. or below in the 3rd and 4th round will not
move on to the next round. For round 5, the players will be given a chance to select 3
factors from the given binomial. However, if they obtain one incorrect factor in this round,
no points will be given. EACH ROUND will be played within 5 MINUTES.
The players must show their solution to make their
answer valid and to consider it for checking.

3. Overview
Guide Card
Activity Card No. 2
Activity Card No. 1
Assessment Card No.1
Assessment Card No.2
Enrichment Card
Answer Card
Reference Card
1
2-4
5-6
7-8
9-10
11-12
13-14
15-17
18

4. LEAST MASTERED SKILL:
Identifying the factored form of
polynomial. (M10AL – Ih – 1)
Subtasks:
Determine whether the given binomial is a factor of
the given polynomial.
Solve the remainder when 𝑃(𝑥) is divided by (𝑥 −
𝑟).
Find the factors of polynomial.
1.
2.
3.

5. (FACTOR THEOREM)
EXAMPLE 1. Show that (𝑥 − 1) is a
factor of 3𝑥3
− 8𝑥2
+ 3𝑥 + 2.
Solution: Using the factor theorem, we
have: x − r ⟹ (𝑥 − 1)
𝑟 = 1
𝑃 1 = 3(1)3 − 8(1)2 + 3 1 + 2
𝑃 1 = 3 1 − 8 1 + 3 + 2
𝑃 1 = 3 − 8 + 3 + 2
𝑃 1 = 0
Since P(1)=0, then (x-1) is a factor of
𝟑𝒙 𝟑
− 𝟖𝒙 𝟐
+ 𝟑𝒙 + 𝟐.
EXAMPLE 2. Show that (𝑥 + 2)
is a factor of 5𝑥2 − 2𝑥 + 1.
Solution: x − r ⟹ 𝑥 + 2
𝑥 + 2 ⟹ [𝑥 − −2 ]
𝑟 = −2
𝑃 −2 = 5(−2)2 − 2 −2 + 1
𝑃 −2 = 5 4 + 4 + 1
𝑃 −2 = 20 + 4 + 1
𝑃 −2 = 25
Since P(-2)=25, (x+2) is NOT a
factor of 𝟓𝒙 𝟐 − 𝟐𝒙 + 𝟏.
If 𝑃 𝑟 = 0, then 𝑥 − 𝑟 is a factor of 𝑃(𝑥)

6. (APPLYING THE RATIONAL ROOT THEOREM
AND FACTOR THEOREM IN FINDING THE
FACTORS OF POLYNOMIAL)
EXAMPLE. Write 𝒙 𝟐 − 𝟔𝒙 + 𝟓 = 𝟎 in factored form.
Identify the DEGREE of the polynomial.
(THIS IS TO DETERMINE THE POSSIBLE NUMBER OF FACTORS)
Determine the LEADING coefficient and the
CONSTANT term.
Get the FACTORS of the leading coefficient and
the FACTORS of the constant term.
Divide the factors of the constant term by the
factors of the leading coefficient to obtain the
value of r.
Apply the concept of factor theorem to check
whether 𝑥 − 𝑟 is a factor of 𝑃(𝑥).
D
LC
F
r
F
1⇒±1 5⇒±1, ±5
𝑟 =
𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑡𝑒𝑟𝑚
𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑙𝑒𝑎𝑑𝑖𝑛𝑔 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
𝟏𝒙 𝟐 − 𝟔𝒙 + 𝟓 = 𝟎
𝒙 𝟐
− 𝟔𝒙 + 𝟓 = 𝟎
Constant
Term
Leading
coefficient
𝑟 =
±1
±1
; 𝑟 =
±5
±1
If 𝑃 𝑟 = 0, then 𝑥 − 𝑟
is a factor of 𝑃(𝑥)
STEPS:REMEMBER ME!
EXAMPLE:

7. (APPLYING THE RATIONAL ROOT THEOREM
AND FACTOR THEOREM IN FINDING THE
FACTORS OF POLYNOMIAL)
EXAMPLE. Write 𝒙 𝟐 − 𝟔𝒙 + 𝟓 = 𝟎 in factored form.
Solution #7: 𝑟 = −5
𝑷 𝟔 = (−𝟓) 𝟐
−𝟔 −𝟓 + 𝟓
𝑃 6 = 25 + 30 + 5
𝑃 6 = 60
Since P(5)≠0, 𝑥 − 𝑟 ⇒ 𝑥 − −5 ⇒ 𝑥 + 5 𝑖𝑠 𝒏𝒐𝒕 𝒂 𝒇𝒂𝒄𝒕𝒐𝒓.
Therefore, the two factors of
𝒙 𝟐
− 𝟔𝒙 + 𝟓 = 𝟎 𝑎𝑟𝑒
𝑥 − 1 𝑎𝑛𝑑 𝑥 − 5 .
Solution #1: 𝑟 = 1
𝑷 𝟏 = (𝟏) 𝟐
−𝟔 𝟏 + 𝟓
𝑃 1 = 1 − 6 + 5
𝑃 1 = 0
Since P(5)≠0, 𝑥 − 𝑟 ⇒ [𝑥 − 1 ] ⇒ (𝑥 − 1)𝑖𝑠 𝒂 𝒇𝒂𝒄𝒕𝒐𝒓.
Solution #3: 𝑟 = 5
𝑷 𝟐 = (𝟓) 𝟐
−𝟔 𝟓 + 𝟓
𝑃 2 = 25 − 30 + 5
𝑃 2 = 0
Since P(5)≠0, 𝑥 − 𝑟 ⇒ [𝑥 − 5 ] ⇒ (𝑥 − 5)𝑖𝑠 𝒂 𝒇𝒂𝒄𝒕𝒐𝒓.
Solution #2: 𝑟 = −1
𝑷 −𝟏 = (−𝟏) 𝟐
−𝟔 −𝟏 + 𝟓
𝑃 −1 = 1 + 6 + 5
𝑃 −1 = 12
Since P(-1)≠0, 𝑥 − 𝑟 ⇒ [𝑥 − −1 ] ⇒ (𝑥 + 1)𝑖𝑠 𝑵𝑶𝑻 𝒂 𝒇𝒂𝒄𝒕𝒐𝒓.

9. A. REMAINDER, REMEMBER???
State whether the given remainder is correct or not. Choose
FACT, if the remainder is correct and BLUFF if it is
incorrect.
1. (𝑥4
−𝑥3
+ 2) ÷ (𝑥 + 2); 𝑅 = 0
2. (𝑥3
−𝑥2
+ 𝑥 + 6) ÷ (𝑥 − 3); 𝑅 = 18
3. (𝑥4
+4𝑥2
− 32) ÷ (𝑥 − 2); 𝑅 = 0
4. (𝑥4
−2𝑥3
+ 2𝑥2
− 1) ÷ (𝑥 − 1); 𝑅 = 2
5. (3𝑥2+5𝑥3 − 8𝑥 − 6) ÷ (𝑥 + 1); 𝑅 = 0
1. (𝑥4
−𝑥3
+ 2) ÷ (𝑥 + 2); 𝑅 = 0
2. (𝑥3
−𝑥2
+ 𝑥 + 6) ÷ (𝑥 − 3); 𝑅 = 18
3. (𝑥4
+4𝑥2
− 32) ÷ (𝑥 − 2); 𝑅 = 0
4. (𝑥4
−2𝑥3
+ 2𝑥2
− 1) ÷ (𝑥 − 1); 𝑅 = 2
5. (3𝑥2+5𝑥3 − 8𝑥 − 6) ÷ (𝑥 + 1); 𝑅 = 0
Tell whether the given remainder is correct or incorrect. Choose FACT,
if the remainder is CORRECT and BLUFF if it is INCORRECT.

11. B. I REMAINDER!!!
Determine the remainder when 𝑃(𝑥) is divided by
the given binomial.
1. (𝑥2−3𝑥 + 7) ÷ (𝑥 + 5)
2. (𝑥4
−𝑥3
+ 2) ÷ (𝑥 − 1)
3. (𝑥3−𝑥2 − 8𝑥 + 12) ÷ (𝑥 − 2)
4. (8𝑥3−4𝑥2 + 2𝑥 − 1) ÷ (2𝑥 − 1)
5. (25𝑥2 − 10𝑥 − 8) ÷ (5𝑥 + 2)
Determine the remainder when 𝑃(𝑥) is divided by
the given binomial.
1. (𝑥2−3𝑥 + 7) ÷ (𝑥 − 5)
2. (𝑥4
−𝑥3
+ 2) ÷ (𝑥 + 1)
3. (𝑥3−𝑥2 − 8𝑥 + 12) ÷ (𝑥 − 2)
4. (2𝑥3+4𝑥2 + 2𝑥 − 1) ÷ (𝑥 + 1)
5. (5𝑥2 − 10𝑥 − 40) ÷ (𝑥 + 2)

13. A. WHAT’s THE FACTor?
Determine the factor of the given polynomial
from the given binomials.
1. 𝑃 𝑥 = 𝑥3 − 7𝑥 + 6
2. 𝑃 𝑥 = 2𝑥3
− 7𝑥 − 2
3. 𝑃 𝑥 = 4𝑥4
− 3𝑥3
− 𝑥2
+ 2𝑥 − 2
4. 𝑃 𝑥 = 𝑥4 + 3𝑥3 − 4𝑥2;
5. 𝑃 𝑥 = 16𝑥4
+ 24𝑥3
+ 4𝑥2
− 2𝑥 − 4;
(𝒙 + 𝟏)
(𝒙 + 𝟐)
(𝒙 − 𝟏)
(𝒙 − 𝟐)
(𝒙 + 𝟏) (𝒙 − 𝟏)
(𝒙 + 𝟒) (𝒙 − 𝟒)
(𝟐𝒙 − 𝟏) (𝟐𝒙 + 𝟏)
1. 𝑃 𝑥 = 𝑥3
− 7𝑥 + 6
2. 𝑃 𝑥 = 2𝑥3
− 7𝑥 − 2
3. 𝑃 𝑥 = 4𝑥4
− 3𝑥3
− 𝑥2
+ 2𝑥 − 2
4. 𝑃 𝑥 = 𝑥4
+ 3𝑥3
− 4𝑥2
;
5. 𝑃 𝑥 = 𝑥4
+ 4𝑥3
+ 4𝑥2
− 2𝑥 − 15;
(𝒙 + 𝟏)
(𝒙 + 𝟐)
(𝒙 − 𝟏)
(𝒙 − 𝟐)
(𝒙 + 𝟏) (𝒙 − 𝟏)
(𝒙 + 𝟒) (𝒙 − 𝟒)
(𝒙 − 𝟑) (𝒙 + 𝟑)
Determine the factor of the given polynomial
from the given binomials.

15. B. I Remainder the FACTor!
Use the Factor Theorem to identify the remainder and
determine whether or not the first polynomial is a factor of
the second.
1. 𝑥 − 1 ; 𝑥2 + 2𝑥 + 5
2. 𝑥 + 1 ; 𝑥4
− 𝑥 − 2
3. 𝑥 − 2 ; 2𝑥3 − 9𝑥2 + 9𝑥 + 2
4. 𝑎 − 1 ; 𝑎3 − 2𝑎2 + 𝑎 − 2
5. 𝑦 + 3 ; 2𝑦3 + 𝑦2 − 13𝑦 + 6
1. 𝑥 − 1 ; 𝑥2 + 2𝑥 + 5
2. 𝑥 + 1 ; 𝑥4
− 𝑥 − 2
3. 𝑥 − 2 ; 2𝑥3
− 9𝑥2
+ 9𝑥 + 2
4. 𝑎 − 1 ; 𝑎3 − 2𝑎2 + 𝑎 − 2
5. 𝑦 + 3 ; 2𝑦3 + 𝑦2 − 13𝑦 + 6
Use the Factor Theorem to identify the remainder and determine
whether or not the first polynomial is a factor of the second.
B. I Remainder the FACTor!

17. Find the 3 factors of the given polynomial.
𝑥3 + 3𝑥2 − 4𝑥 − 12
(𝑥 − 1)
(𝑥 + 1)
(𝑥 + 2)
(𝑥 − 2)
(𝑥 + 3)
(𝑥 − 3)
(𝑥 + 4)
(𝑥 − 4) (𝑥 + 6)
(𝑥 − 6)
I FACTor!
Find the 3 factors of the given polynomial.

19. BLUFF BOARD
1. BLUFF; R=26
2. BLUFF; R=27
3. FACT
4. BLUFF; R=0
5. FACT
ACTIVITYCARDNO. 1
1. R=17
2. R=4
3. R=0
4. R=-1
5. R=0
ACTIVITYCARDNO. 2

20. BLUFF BOARD
1. (𝑥 − 1)
ASSESSMENT CARD
NO. 1
2. (𝑥 − 2)
3. (𝑥 − 1)
4. (𝑥 + 4)
5. (𝑥 + 3)
1. 𝑅 = 8; 𝑁𝑂𝑇 𝐴 𝐹𝐴𝐶𝑇𝑂𝑅
ASSESSMENT CARD
NO. 2
2. 𝑅 = 0; 𝐹𝐴𝐶𝑇𝑂𝑅
3. 𝑅 = 0; 𝐹𝐴𝐶𝑇𝑂𝑅
5. 𝑅 = 0; 𝐹𝐴𝐶𝑇𝑂𝑅
4. 𝑅 = −2; 𝑁𝑂𝑇 𝐴 𝐹𝐴𝐶𝑇𝑂𝑅
ENRICHMENT
CARD
(𝑥 − 2)
(𝑥 + 2)
(𝑥 + 3)

21. ENRICHMENTCARD
(𝑥 − 1)
(𝑥 + 1)
(𝑥 − 2)
(𝑥 + 3)
(𝑥 − 4)
REFERENCECARD
Mathematics – Grade 10
Learner’s Module
First Edition
https://www.brightstorm.com/math/algebra-
2/factoring/rational-roots-theorem/
Mathematics for the 21st Century Learner
Grade 10
DIWA TEXTBOOK

22. or
(FACTORS OF POLYNOMIAL)
ALL RIGHTS RESERVED 2019