Factoring general trinomials

Prepared by: Gauben L. Malicsi

To factor trinomials with 1 as the numerical coefficient of the leading
term:
a. Factor the leading term of the trinomial and write these factors
as the leading terms of the factors;
b. List down all the factors of the last term;
c. Identify which factor pair sums up to the middle term; then
d. Write each factor in the pairs as the last term of the binomial
factors.
To factor trinomials with more than 1 as the numerical coefficient of
the leading term:
a. Find the product of the leading term and the last term.
b. Find the factors of the product whose sum is equal to the middle
term
c. Rewrite the trinomial as a four-term expression by replacing the
middle term with the sum of the factors.
d. Group terms with common factors.
e. Factor the groups using greatest common monomial factor.
f. Factor out the common binomial factor and write the remaining
factor as a sum or difference of the common monomial factors.
EXAMPLE 6:
Factoring general trinomial with leading coefficient 1
Factor each polynomial.
a. 𝑝2
+ 5𝑝 + 6 b. 𝑥2
+ 8𝑥 − 9
SOLUTIONS:
a. List all the possible factors
of 6.
Factors of 6
2 and 3 -2 and -3
6 and 1 -6 and -1
 Find factors of 6 whose sum is 5.
2 + 3 = 5 (-2) + (-3) = -5
6 + 1 = 7 (-6) + (-1) = -7
 Thus, the factor of 𝑝2
+ 5𝑝 + 6 =
(𝒑 + 𝟐)(𝒑 + 𝟑)
b. List all the possible factors
of -9.
Factors of -9
-3 and 3 -9 and 1
3 and -3 9 and -1
 Find factors of -9 whose sum is 8.
(-3) + 3 = 0 (-9) + 1 = -8
3 + (-3) = 0 9 + (-1) = 8
 Thus, the factor of 𝑥2
+ 8𝑥 − 9 =
( 𝒙 + 𝟗)(𝒙 − 𝟕)
EXAMPLE 7:
Factoring general trinomial with leading coefficient greater than 1
Factor each polynomial.
a. 6𝑥2
− 5𝑥 − 6 b. 2𝑦2
− 11𝑦 + 12
SOLUTIONS:
a. 6𝑥2
− 5𝑥 − 6
 Find the product of the leading term and the last term.
(6𝑥2
)(−6) = −36𝑥2
 Find the factors of −36𝑥2
whose sum is -5x.
(-6x) + 6x = 0 (-9x) + 4x = -5x (-36x) + x = -35x
6x + (-6x) = 0 9x + (-4x) = 5x 36x + (-x) = 35x
Factoring general trinomials
Factors
completely
general
trinomials
COMPETENCY 1.5

 Rewrite the trinomial as a four-term expression by replacing the
6𝑥2
− 9𝑥 + 4𝑥 − 6
 Group terms with common factors.
(6𝑥2
− 9𝑥) + (4𝑥 − 6)
 Factor the groups using greatest common monomial factor.
3x(2x – 3) + 2(2x – 3)
 Factor out the common binomial factor and write the remaining factor
as a sum or difference of the common monomial factors.
(2x – 3)(3x + 2)
b. 2𝑦2
− 11𝑦 + 12
 Find the product of the leading term and the last term.
(2𝑦2
)(12) = 24𝑦2
 Find the factors of 24𝑦2
whose sum is -11y.
(-6y) + (-4y) = -10y (-8y) + (-3y) = -11y (-24y) + (-x) = -25y
6y + 4y = 10y 8y + 3y = 11y 24y + y = 25y
 Rewrite the trinomial as a four-term expression by replacing the
2𝑦2
− 8𝑦 − 3𝑦 + 12
 Group terms with common factors.
(2𝑦2
− 8𝑦) − (3𝑦 + 12)
 Factor the groups using greatest common monomial factor.
2y(y – 4) - 3(y – 4)
 Factor out the common binomial factor and write the remaining factor
as a sum or difference of the common monomial factors.
(y – 4)(2y – 3)
PERFORMANCE TASK:
Direction: Make your own examples of general trinomials including the
factored form.
1 as leading coefficient More than 1 as leading coefficient
Example Factored form Example Factored form
ASSESSMENT TASK:
Show your solutions on the box provided below and write your final
answer on the space before the number.
1. Factor each polynomial. (See Example 6)
a. 𝑥2
+ 9𝑥 + 18
b. 𝑦2
− 2𝑦 − 24
c. 𝑤2
+ 3𝑤 − 10
2. Factor each polynomial. (See Example 7)
a. 2𝑚2
+ 9𝑚 + 4
b. 6𝑡2
− 𝑡 − 15
YOUR SOLUTIONS:
1. 2. 3.
4. 5.

INDICATORS Meets
Standard of
Excellence
Approaching
Standard of
Excellence
Meets
Acceptable
Standard
Does Not Meet
Acceptable
Standard
CRITERIA 4 3 2 1
Performance
Task
Shows
exemplary
performance
Demonstrates
solid
performance
and
understanding
With some
errors and
mastery is
not
thorough.
Has errors,
omission and
misconception.
Assessment
Task
With 5
correct
answers
With 4
correct
answers
With 3
correct
answers
With less than
3 correct
answers
Completeness Has all
aspects of
work that
exceed level
of
expectation
Has some
aspects of
work that
exceed level
of
expectation
Has minimal
aspects of
work that
meet level
of
expectation
No aspect of
work meets
level of
expectations
Neatness The learning
tasks are
done very
neatly.
The learning
tasks are
done neatly.
The learning
tasks are
done quite
neatly.
The learning
tasks are
poorly done
and need
improvement.
Submission of
Requirements
The assigned
learning
tasks are
submitted on
or before
the
deadline.
The assigned
learning
tasks are
submitted a
day after the
deadline.
The assigned
learning
tasks are
submitted
two days
after the
deadline.
The assigned
learning tasks
are submitted
three days
after the
deadline.
TOTAL SCORE
_________________________________ _________________________________
Parent/Guardian’s Signature Over
Printed Name
Student’s Signature Over Printed
Name

Factoring general trinomials

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