Factoring Perfect Square Trinomial

In Mathematics

VIII

Strategic Intervention Material

Prepared by:

SHERYL B. DELA CRUZTeacher I

GUIDE CARDLeast Mastered Skill: Factoring Perfect Square Trinomial.

Sub tasks:

Determine whether the given algebraic expression is perfect square trinomial or not.

Complete the terms of the expression in the product of the given factor of perfect square trinomial..

Give the missing factor of the perfect square trinomial

Determine the Factor of perfect square trinomial.

Perfect Square Trinomial

What is Perfect Square Trinomial?

A PERFECT SQUARE TRINOMIAL is the result of squaring a binomial.

Example: (x + y)2 or (x + y) (x + y) = x2 + 2xy + y2

Therefore, x2 + 2xy + y2 is a PERFECT SQUARE TRINOMIAL! Correct!

Activity Card 1Complete Me!Direction : Complete the terms. Write your answer in the space provided.

1. (x-y)(x-y) = x2 – 2xy + _______ 2. (2m+5)(2m+5) = _____ +20m + _____

3. (x+6)2 = x2 + _____ + _______ 4. (3a - 2)2 = _____ - 12a + ______

Identifying Perfect Square TrinomialA PERFECT SQUARE TRINOMIAL has FIRST and LAST terms which are PERFECT SQUARE, and a MIDDLE term is twice the product of the square root of the FIRST and LAST terms.

Example : x2 + 6x + 9 is Perfect Square Trinomial, because X2 and 9 are Perfect Square = X 6x is 2 ( X )( 3 ) = 3

How do we easily identify if the given trinomial is a Perfect Square? Or not?

First Term Last Term

MiddleTermFirst TermLast Term

MiddleTerm

Activity Card # 2

Am I Perfect Square Trinomial or not?

Direction: Write PST if the given expression is Perfect Square Trinomial and NOT PST if the given expression is not Perfect Square Trinomial.x2 + 4x + 41

.

4x2 + 5x + 1 x2 – 24x + 36

6x2 – 9x + 8481x2 - 126x + 499x2 + 24x + 14

2.

3.

4.

5.

6.

To factor Perfect Square Trinomial:Example: x2 + 18x + 81

1. Get the square root of the first term and the last term. = x = 9

2. List down the square root as sum or difference of two terms as the case may be.

(x+ 9)2 or (x+9) (x+9)

Is there any pattern in factoring

Perfect Square Trinomial?

YES! You may use the following relationship to factor:

(1st term)2 + 2(1st term)(last term) + (last term)2 = (1st + last)2

(1st term)2 - 2(1st term)(last term) + (last term)2 = (1st - last)2Example!

X2 – 14x + 49 = (x – 7)2 or (x-7)(x-7) X2 72

2 (x) (7) = 14x

First Term 2nd Term Last/3rdTerm

Fill Me!Activity Card # 3

Direction: Give the missing factor of Perfect Square Trinomial.

1. x2 + 2x + 1 = (_____) (x + 1)

3. 9x4 - 24x + 16y2 = (3x2 – 4y) (____)

4. 16x2 + 24x + 9 = (____) (____)

2. 4x2 - 12x + 9 = (2x - 3) (____)

ACTIVITY CARD # 4

True or

False

1. 9x2 + 4x + 1 = (3x+1)2

2. 4x2 - 16x + 16 = (2x-4)2

3. x2 + 14x + 49 = (x-7)2

4. 16x2 - 24x + 9y2 = (4x-3y)2

Direction: Write TRUE if the corresponding factor is correct and FALSE if it is not.

What is My Factor?

1. 4x2 – 16x + 16 = ________________

2. x2 + 12x + 36 = ________________

3. x2 – 14x + 49 = ________________

4. 9x2 + 6xy + y2 = ________________

5. x2 – 10x + 25 = ________________

ACTIVITY CARD # 5

Direction : Give the factor of the following Perfect Square Trinomial.

Enrichment Card

Is it possible, to find the measure of the sides

of my square garden,

if my garden’s area

is 4x2 – 12x + 9? Can you help me?

Direction : Encircle the letter of the correct answer.

1. Which of the following factors give a product of x2 +6x+9?

a. (x+3)(x-3)

b. (x+3)(x+3)

c. (x+3)(x+2)

d. (x+6)(x+3)

2. Which of the following is perfect square trinomial?

a. x2 + 3x + 16

b. x2 -18x + 9

c. x2 + 2x +1

d. 25 x2 + 25x +4

3. Which of the following values of k will make x2 +8x + k perfect square trinomial?

a. -16

b. 16

c. 64

d. -64

4. Which of the following is Correct?

a. x2 +4x+4 = (x+4)2

b. X2 -12x +36 =(x+2)(x-6)

c. X2 +7x + 49 = (X+ 7)(x-7)

d. X2 -10x+25 =(x-5)2

5. What is the factor of 64x2 +16x +1?

a. (8x+1)2

b. (8x -1)(8x+1)

c. (8x -1)2

d. (8x-2) (8x+2)

Assessment Card

References

ScoresActivity 1____Activity 2____Activity 3____Activity 4____Activity 5____Assessment____Enrichment____