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Factors of Polynomials
Factoring a Perfect
Square Trinomial
Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile
OBJECTIVES:
1. recall the concept of a
perfect square
2. identify a perfect
square trinomial
3. use MBM methodology
to factor perfect
square trinomial
REVIEW
Answer:
The square of a number is the number
times itself.
Question:
What is the square of a number?
REVIEW
Answer:
1. The 1st and the last term are perfect square.
2. The middle term is twice the product of the
first and the last term.
Question:
How can you tell if it is a perfect
square trinomial?
This is how Perfect Square Trinomial looks like.
Activity 1 Find the perfect me!
10x 81 18x X2 4
15x 16x2 -24x 9 10x 28x
4x2 -16x 16 15x 25 49x2
16x2 49 8x 16 24x2 9
25 14x 8x 40x 30x 10x
7x x2 12x 25x2 40 12x2
Description: Look for the different perfect square trinomials found in the box.
Answers might be in diagonal, horizontal or vertical in form.
Answer in Activity 1 Find the perfect me!
10x 81 18x X2 4
15x 16x2 -24x 9 10x 28x
4x2 -16x 16 15x 25 49x2
16x2 49 8x 16 24x2 9
25 14x 8x 40x 30x 10x
7x x2 12x 25x2 40 12x2
Description: Look for the different perfect square trinomials found in the box.
Answers might be in diagonal, horizontal or vertical in form.
Remember: You can use the following
relationships to factor perfect square trinomials:
Remember to factor out first the greatest common monomial
factor before factoring the perfect square trinomial.
(First term)2 + 2(First term)(Last term) + (Last term)2 = (First term + Last term)2
(First term)2 – 2(First term)(Last term) + (Last term)2 = (First term – Last term)2
Illustrative Examples:
1. Factor n2 + 16n + 64
Multi Breaker Map
Direction: Factor the following perfect square trinomial using MBM.
Get the square root of the first term: Get the square root of the last term:
√ n2 = n √64 = 8
Check if the middle term is twice the product of the 1st and last term:
16n = 2(n.8)
If the three verifications are satisfied then it’s a PST. Add the factor
of the 1st and last term then squared:
(n + 8)2
2. Factor 4r2 – 12r + 9
Multi Breaker Map
Direction: Factor the following perfect square trinomial using MBM.
Get the square root of the first term: Get the square root of the last term:
√ 4r2 = 2r √9 = 3
Check if the middle term is twice the product of the 1st and last term:
12r = 2(2r . 3)
If the three verifications are satisfied then it’s a PST. Subtract the
factor of the 1st and last term then squared:
(2r - 3)2
3. Factor 75t3 + 30t2 + 3t
Get the square root of the first term: Get square root of the last term:
√25t2 = 5t √1= 1
Check if the middle term is twice the product of the 1st and last term:
10t = 2(5t . 1)
If the three verifications are satisfied then it’s a PST. Add the factor
of the 1st and last term then squared:
(5t + 1)2
Find the common monomial factor to of the trinomial then simplify:
(75t3 + 30t2 + 3t)/3t = 25t2 + 10t + 1
Multiply the factor by 3t to equate the trinomial:
3t(5t + 1)2
Activity 2: To Do….
Group Activity Let’s MBM!
Direction: Group the students into 5 groups.
Factor any two numbers using MBM.
1. 121c4 + 66c2 + 9
2. 25r2 + 40rn + 16n2
3. 16x2 + 56x + 49
4. 18h2 + 12h + 2
5. 20f 4 – 60f 3 + 45f 2
Thank you!
Learning Resources:
Grade 8 Math Time
k-to-12-grade-8-math-learner-module
https://www.google.com/search?q=perfect+squar
e+trinomial&rlz=1C1GCEU_enPH821PH821&sxsrf=
ALeKk01FvBiKmtzMSx1P_yasB7YN2q6OGg:158908
9125111&tbm=isch&source=iu&ictx=1&fir=s7xEYX
LPsPU05M%253A%252CknBc5lKKuTwkIM%252C_
&vet=1&usg=AI4_-
kRLHyz7RChJG0o2UGvenfqB0bW5HA&sa=X&ved=
2ahUKEwj3-
sWmyqjpAhXOxIsBHZseAuUQ9QEwFXoECAUQIA#i
mgrc=s7xEYXLPsPU05M:

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factoring perfect square trinomial

  • 1. Factors of Polynomials Factoring a Perfect Square Trinomial
  • 2. Jessebel G. Bautista Antonio J. Villegas Voc’l High School My Profile
  • 3. OBJECTIVES: 1. recall the concept of a perfect square 2. identify a perfect square trinomial 3. use MBM methodology to factor perfect square trinomial
  • 4. REVIEW Answer: The square of a number is the number times itself. Question: What is the square of a number?
  • 5. REVIEW Answer: 1. The 1st and the last term are perfect square. 2. The middle term is twice the product of the first and the last term. Question: How can you tell if it is a perfect square trinomial?
  • 6. This is how Perfect Square Trinomial looks like.
  • 7. Activity 1 Find the perfect me! 10x 81 18x X2 4 15x 16x2 -24x 9 10x 28x 4x2 -16x 16 15x 25 49x2 16x2 49 8x 16 24x2 9 25 14x 8x 40x 30x 10x 7x x2 12x 25x2 40 12x2 Description: Look for the different perfect square trinomials found in the box. Answers might be in diagonal, horizontal or vertical in form.
  • 8. Answer in Activity 1 Find the perfect me! 10x 81 18x X2 4 15x 16x2 -24x 9 10x 28x 4x2 -16x 16 15x 25 49x2 16x2 49 8x 16 24x2 9 25 14x 8x 40x 30x 10x 7x x2 12x 25x2 40 12x2 Description: Look for the different perfect square trinomials found in the box. Answers might be in diagonal, horizontal or vertical in form.
  • 9. Remember: You can use the following relationships to factor perfect square trinomials: Remember to factor out first the greatest common monomial factor before factoring the perfect square trinomial. (First term)2 + 2(First term)(Last term) + (Last term)2 = (First term + Last term)2 (First term)2 – 2(First term)(Last term) + (Last term)2 = (First term – Last term)2
  • 10. Illustrative Examples: 1. Factor n2 + 16n + 64 Multi Breaker Map Direction: Factor the following perfect square trinomial using MBM. Get the square root of the first term: Get the square root of the last term: √ n2 = n √64 = 8 Check if the middle term is twice the product of the 1st and last term: 16n = 2(n.8) If the three verifications are satisfied then it’s a PST. Add the factor of the 1st and last term then squared: (n + 8)2
  • 11. 2. Factor 4r2 – 12r + 9 Multi Breaker Map Direction: Factor the following perfect square trinomial using MBM. Get the square root of the first term: Get the square root of the last term: √ 4r2 = 2r √9 = 3 Check if the middle term is twice the product of the 1st and last term: 12r = 2(2r . 3) If the three verifications are satisfied then it’s a PST. Subtract the factor of the 1st and last term then squared: (2r - 3)2
  • 12. 3. Factor 75t3 + 30t2 + 3t Get the square root of the first term: Get square root of the last term: √25t2 = 5t √1= 1 Check if the middle term is twice the product of the 1st and last term: 10t = 2(5t . 1) If the three verifications are satisfied then it’s a PST. Add the factor of the 1st and last term then squared: (5t + 1)2 Find the common monomial factor to of the trinomial then simplify: (75t3 + 30t2 + 3t)/3t = 25t2 + 10t + 1 Multiply the factor by 3t to equate the trinomial: 3t(5t + 1)2
  • 13. Activity 2: To Do…. Group Activity Let’s MBM! Direction: Group the students into 5 groups. Factor any two numbers using MBM. 1. 121c4 + 66c2 + 9 2. 25r2 + 40rn + 16n2 3. 16x2 + 56x + 49 4. 18h2 + 12h + 2 5. 20f 4 – 60f 3 + 45f 2
  • 15. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module https://www.google.com/search?q=perfect+squar e+trinomial&rlz=1C1GCEU_enPH821PH821&sxsrf= ALeKk01FvBiKmtzMSx1P_yasB7YN2q6OGg:158908 9125111&tbm=isch&source=iu&ictx=1&fir=s7xEYX LPsPU05M%253A%252CknBc5lKKuTwkIM%252C_ &vet=1&usg=AI4_- kRLHyz7RChJG0o2UGvenfqB0bW5HA&sa=X&ved= 2ahUKEwj3- sWmyqjpAhXOxIsBHZseAuUQ9QEwFXoECAUQIA#i mgrc=s7xEYXLPsPU05M: