The document outlines the steps to solve quadratic equations by factoring perfect square trinomials, emphasizing criteria such as having three terms, and that both the first and last terms must be perfect squares. It details step-by-step processes including converting equations to standard form, computing square roots, determining the relationship between terms, and applying the zero product property. Additionally, it includes examples to illustrate the method and a task to identify quadratic equations related to the difference of two squares.

1. Solving Quadratic
Equations by Factoring
PERFECT SQUARE TRINOMIALS

2. Recognizing Perfect Square Trinomials
1. Must have three terms.
2. The first and third term must be a perfect square.
3. The middle term must be twice the product of the
square roots of the first and last terms.

3. Step 1: Transform the equation into its Standard Form.
Steps in Solving Quadratic Equations by Factoring
(Perfect Square Trinomials)
Step 2: Inspect if the first and last terms are perfect squares and positive.
Step 3: Get the square root of the first term.
Step 4: Get the square root of the second term.
Step 5: Look at the middle term if it is twice the product of the square roots of
the first and last terms.
Step 6: Express the factor as a square of a binomial. The sign in between the
binomial depends on the sign of the middle term of the perfect
square trinomial. The terms in the binomial are the square roots of
the first and last terms of the perfect square trinomial.
Step 7: Apply the zero product property.

4. 1. x2
- 24x = -144
= x
= 12
x2
- 24x + 144 = 0
(2)(x)(12) =
( - )( - ) = 0
x x 12
12
(x - 12)2
= 0
x - 12 = 0 x - 12 = 0
x = 12 x = 12
Step 1: Transform the equation into its Standard Form.
Step 2: Inspect if the first and last terms
are
perfect squares and positive.
Step 3: Get the square root of the first term.
Step 4: Get the square root of the second term.
Step 5: Look at the middle term if it is twice the
product of the square roots of the first and last terms.
Step 6: Express the factor as a square of a binomial.
The sign in between the binomial depends on the sign
of the middle term of the perfect square trinomial.
The terms in the binomial are the square roots of the
first and last terms of the perfect square trinomial.
Step 7: Apply the zero product property by equating
each factor to zero.
24x

5. 2. x2
+ 4x + 4 = 0
= x
= 2
(2)(x)(2) =
( + )( + ) = 0
x x 2
2
(x + 2)2
= 0
x + 2 = 0 x + 2 = 0
x = -2 x = -2
Step 1: Transform the equation into its Standard Form.
Step 2: Inspect if the first and last terms
are
perfect squares and positive.
Step 3: Get the square root of the first term.
Step 4: Get the square root of the second term.
Step 5: Look at the middle term if it is twice the
product of the square roots of the first and last terms.
Step 6: Express the factor as a square of a binomial.
The sign in between the binomial depends on the sign
of the middle term of the perfect square trinomial.
The terms in the binomial are the square roots of the
first and last terms of the perfect square trinomial.
Step 7: Apply the zero product property by equating
each factor to zero.
4x

6. 3. t2
– 16 = 8t Step 1: Transform the equation into its Standard Form.
Step 2: Inspect if the first and last terms
are
perfect squares and positive.
t2
– 8t – 16 = 0
Not applicable because the last term is negative.

7. Identify whether the following Quadratic
Equation is a perfect square trinomial.
1. = -16
2. = 0
3. = 0
4. 0
5. = -36
Assignment:
Solve for the value of
x for those that are
difference of two
squares.
(r2
- 4)
(x − 7)
NO
(x + 1)
NO