This document provides instructions for teaching students about factoring quadratic trinomials. It explains that the product of two binomials with a common term, such as (a + b)(a + c), can be expressed by the formula a2 + (b + c)a + bc. This formula results in a quadratic trinomial since it has three terms. The factors of the trinomial are simply the reverse of this formula. Students are guided through examples of factoring various quadratic trinomials and then do a group activity to practice factoring more examples. They then present their work, followed by a quiz and assignment to further their understanding.

1. Topic: Factors of a Quadratic Trinomial
OBJECTIVE: State how the product of two binomials with a common term expressed by the formula (a +
b) (a + c) = a2 + (b + c)a + bc, is a quadratic trinomial and how the factors of such formula
will just be the reverse, which is a2 + (b + c)a + bc = (a + b) (a + c).
Time: 1 hour
Materials: Textbook to check facts, white board or black board, writing pen or chalk, flash cards.
Procedure:
1. What do you know about binomials a polynomial, factors, addends, a formula? Guide the
students to remember this prerequisite concepts and skills to help them understand better on
this topic.
 Binomial - a polynomial of two terms which indicates the sum or difference of such
terms. Example: x + y; a-b; 2x-5.
 Polynomial - an element from a set of real numbers or variables or the result of
adding, subtracting, multiplying or taking the opposite of the elements. Example: y2 – y
+ 9 is a polynomial with elements from the two sets on which the indicated operations
have been carried out as much as possible. It is also an expressions that can have
constants, variables, exponents but:
 no division by a variable.
 a variable’s exponent can only be 0,1,2,3 etc..
 it can’t have an infinite number of terms
exponents: 0,1,2,3…
3xy-2
5xy2 – 3x + 5y3 – 3
2
X + 2
Terms
A Polynomial Not A Polynomial

2.  Factor – any one set of the numbers or expressions multiplied together to form a
product. Thus 6 and 4 are factors of 24 and a and b are factors of ab.
 Addends – any number that are added together.
Example 8 + 3 = 11, the 8 and the 3 are addends.
 Formula – a rule expressed in symbols. Example: A = l x w (the area of the rectangle
equals the length times the width.
2. How is the product of two binomials with a common term expressed by the formula (a + b) (a +
c) = a2 + (b + c)a + bc, is a quadratic trinomial and how the factors of such formula will just be
the reverse, which is a2 + (b + c)a + bc = (a + b) (a + c).
Example:
The factors of x2 - 9x + 20
are two binomials: (x - 5) (x – 4)
whose first terms are √x2: (x) (x)
and whose second terms are: (-4)(-5)
both addends of -9 and factors of 20
3. Explain further how the formula (a + b) (a + c) = a2 + (b + c)a + bc becomes quadratic and a
trinomial since it becomes trinomial because there are three in terms in a polynomial.
This makes it a quadratic
a2 + (b + c)a + bc
4. Factor these polynomials:
a.) x2 + 9x + 20 c.) x2 – 8x -20
ans. (x + 5) (x + 4) ans. (x – 10) (x + 2)
b.) x2 – 9x + 20 d.) x2 + 8x - 20
ans. (x – 5) (x – 4) ans. (x + 10) (x – 2)

3. 5. Activity:
Divide the class into as many groups and have them analyze and factor the following quadratic
polynomials. Give them roughly 5 minutes to do this group activity.
Group 1: x2 – 9x + 14 and m2 – 5mp – 14p2
Group 2: y2 – 11y – 12 and 4x2 – 14xy + 6y2
Group 3: a2 + 4a – 12 and m2 – 5m + 4
Group 4: 4x + 15X + 9 and y2 – 3y - 28
Group 5: x + 10x + 9 and 9n2 + 12n – 12
6. Get a representative from each group to come up to the front of the board to explain and
record their solution to the problem.
7. Evaluation about Factoring
Quiz will be given after the whole discussion and activity. Checking of paper and giving of
rationale regarding the topic will be followed. This will be an avenue for them to clarify some
terms regarding the topic.
8. Assignment:
Study in advance the product of binomials with similar terms on page 161 – 163 and answer
questions 1 – 10 (Reference: Basic Algebra for Secondary Schools, LIMJAP)