Topics: Factoring polynomials using various
technique
Vocabulary to use:
factors
prime
factored form
irreducible polynomials
I. Factoring the Greatest Common Factor
Factor and rewrite the problem using the GCF , then use the Distributive property
in
reverse to factor out the GCF.
Ex. 3x + 15 =
Ex. 4y3+10y2 + 2y =
Ex. 3m3+ 6m2 + 9 =
Ex. 3x + 3y + cx + cy =
*Don’t leave out the 1 when factoring out the entire term.
*Check by multiplying the factors back to get the original problem.
II. Factoring by Grouping (p. 38)
The “Factoring by Grouping” method groups the first two terms and the second two
terms, then follows with a greatest common factor of a parentheses within the
two
groups.
Ex. 3a2 −bc + 3b − a2c =
*Notice that the problem doesn’t begin so that you can
find a Greatest Common Factor
from the first two and second two terms. Rearrange the terms so that a GCF shows
up.
III. Factoring Trinomials by Trial -and-Error(p. 39)
Recall factoring by FOIL from factored form (ax + b)(cx +
d).
Ex. 3x2 + 5x − 2 =
Find the factors of the product ac and the factors of the product bd. Focus on
the
coefficient of the middle (x) term.
Ex. 2y2 − 7y + 3 =
IV. Factoring Special Patterns (pp. 40 - 41)
A. Perfect Square Trinomials: x2 + 2xy + y2 = (x + y)2 and x2 − 2xy + y2 = (x −
y)2
Ex. 4t2 +12t + 9=
B. Difference of Two Squares : x2 − y2 = (x + y)(x − y)
Ex. 9r2 −1=
C. Omit Difference and Sum of Two Cubes (p.42, example #6)
(Tape 12:25 – 14:25)
V. Factoring by Substitution (p. 42)
Substitute another variable to replace (always) the middle
term’s variable factor. Factor
the easier problem, then substitute back to get the original problem’s answer.
Ex. m4 − 3m2 −10 =
Let y = m2
VI. Summary of Factoring:
1. First look for _______, if there is one.
2. How many _____________ in the polynomial?
A.4or more—use _________________
B. 3 terms—use ___________ backwards or special factoring
patterns.
.
C. 2 terms—difference of two squares or prime
3. Use ______________ to help with the more complex
factoring problems.
*4. Some students may have learned another approach to
factoring a trinomial that is
called the ac method. The videos do not cover this approach, but you can stop by
the
Tutoring Center to find out about it.
Ex. 6a2 − 48a −120=
Assignments:
Text: pp. 43 – 45 #1 – 21 every other odd, 23 – 39 eoo, 43 – 51 odd, 63, 79,
81, 83
“A Review of Algebra ”: pp. 98 – 100 #5 – 25 odd, 35 – 43 odd, 65, 67, 79, 81
p. 105 #9 – 29 odd, 47, 49
