Download Name: Date: Unit 4 Algebra: Cubic, Square Root, and Rational

Name: ______________________________________
Date:________________
Unit 4 Algebra: Cubic, Square Root, and Rational Functions (Red)
Section 3.2
Factoring Cubics Using Special Product Patterns
Pages 130-133
Essential Question: How do you factor cubics using special product patterns?
Remember: x2 + 2xy + y2 = (x + y)2
Perfect Square Trinomial
Perfect Square Trinomial
Difference of two squares
x – 2xy + y = (x – y)
x2 – y2 =
(x + y) (x - y)
2
2
2
Vocabulary:
Special Product Patterns- there are similar formulas for factoring special cubic polynomials
1.
____________________ = _______ + _______ + _______ + _______
2. ____________________ = _______ - _______ + ______ - _______
Note: the 2nd and 3rd terms both have 3 as a factor
Example 1:
SPECIAL PRODUCT PATTERNS
1. Using special product patterns factor the expression by dividing the 2nd and 3rd term by 3 and take the
cube root of the 1st and 4th term.
x3 + 6x2 + 12x + 8 =
Take the cube root
(___)3 + (3) __ __ + (3) __ __ + (____)3
Divide by 3
2. Now use the above pattern (see definition) to solve:
=
(_____ + ____)3
YOU TRY…
Factor the expressions:
Remember to take the cube root of the 1st and 4th term and divide the 2nd and 3rd term by 3.
a)
x3 – 12x2 + 48x – 64 =
=
b)
x3 + 3x2 + 3x + 1=
=
(___)3 - (3) __ __ + (3) __ __ - (____)3
(_____ - ____)3
(___)3 + (3) __ __ + (3) __ __ + (____)3
(_____ + ____)3
Name: ______________________________________
Date:________________
Example 2:
FACTOR OUT A GCF FIRST
Before factoring using the special products pattern, factor (divide) the GCF first so that the leading coefficient
becomes 1 and the degree is 3.
2x3- 6x2 + 6x - 2 = ___ [(___)3 - (3) ____ + (3) ____ - (____)3]
= ___(_____ - ____)3
YOU TRY…
Factor the expressions:
a) -3x3 + 18x2 - 36x + 24
b) x4 + 15x3 + 75x2 + 125x
Example 3:
FACTORING CUBICS WITH SPECIAL PATTERNS
Combine your knowledge of special patterns and factoring the GCF to solve the following problems:
a3b3 + 12a2b2 + 48ab + 64 =
(___)3 + (3) __ __ + (3) __ __ + (____)3
hint: check to see if you can factor out the GCF, then divide the 2nd & 3rd terms by 3 and
take the cube root of the 1st & 4th term.
=
(_____ + ____)3
hint: use the above patterns to solve
343x3 - 147x2 y+ 21xy2 - y3=
(___)3 - (3) ____ + (3) ____ - (____)3
hint: once again, check to see if you can factor out the GCF, then divide the 2nd & 3rd terms by 3
and then take the cube root of the 1st & 4th term. Use the patterns to solve.
=
(_____ - ____)3
YOU TRY…
Factor the expressions:
a) 8x3 + 12x2y + 6xy2 + y3
b) p3q3- 18p2q2 + 108pq - 216