5­4­16 Alg L Day 3 ­ Factor Completely.notebook
May 04, 2016
will be collected and graded
Do Now: Solve for x
1) x 3
=
60 20
2) 2x + 12 2
=
3 3
Factor
3) x2 + 11x + 24
4) c2 + 2c ­ 35
5) 2x ­ 4x3 6) 21r3s2 + 14r2y2 Factoring
Completely
Day 2
Date: ______
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
May 04, 2016
To factor a polynomial completely (more than
one type of factoring in one question):
1. Look for GCF 1st, then D2PS,and lastly a
Trinomial.
2. Factor the polynomial in that order.
3. Write the answer as the product of all of
the factors. Check.
Meet Mr. & Ms. Factor Face
G
C
D
F
T r i
G
C
D
F
T r i
They will help you factor!
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
May 04, 2016
Today we will use
GCF and Trinomial factoring to
Factor Completely.
Example 1
Factor: 3x2 + 18x + 24
1) Find the GCF and factor
3(x2 + 6x + 8)
it out.
2) Bring down the 3 and factor
the trinomial.
3) You're finished. The answer
has 3 factors!
4) Multiply to check.
3(x + 2)(x + 4)
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
Example 2
Factor:
May 04, 2016
5x2 - 10x + 5
1) Find and factor out the GCF.
5(x2 - 2x + 1)
2) Bring down the 5 and factor
5(x - 1)(x - 1)
the trinomial.
3) You're finished. The answer has
three factors.
4) Multiply to check.
Example 3
Factor:
1) Find and factor out
x3 + 7x2 + 10x
x(x2 + 7x + 10)
the GCF.
2) Bring down the x and
factor the trinomial.
3) You're finished.
4) Multiply to check.
x(x + 2)(x + 5)
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
May 04, 2016
Procedure Summary: To Factor a polynomial completely;
1) Look for the greatest common factor. If there is one,
factor the given polynomial. Then examine each factor.
2) If any of these factors is a binomial, see whether it is
a difference to two squares. If so, factor it as such.
3) If any of these factors is a trinomial, see whether it
can be factored. If so, find its binomial factors.
4) Write the answer as the product of all the factors.
Let's Practice:
1) 3x2 + 18x + 15
GCF___
List factors of ___
GCF___
2) 2x2 - 10x + 8
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
3) 4x2 - 8x - 32
May 04, 2016
GCF___
List factors of ___
4) d3 + 6d2 - 16d
GCF___
List factors of ___
5) a3 - 10a2 + 9a
GCF___
List factors of ___
6) 3x3 - 12x2 - 36x
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
7) 2ax2 + 6ax - 36a
May 04, 2016
GCF___
List factors of ___
8) d3 ­ 8d2 + 16d
GCF___
List factors of ___
9) 2x2 + 14x + 12
GCF___
List factors of ___
10) 4x2 - 40x + 84
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
11) 3x 2y + 9xy - 30y
May 04, 2016
GCF___
List factors of ___
12) 5ax 2 - 10ax - 75a
GCF___
List factors of ___
Independent
Practice Day 2
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
1) 2a2 + 14a + 24
GCF___
List factors of ___
3) 3y2 + 24y + 36
GCF___
List factors of ___
May 04, 2016
2) 7x2 - 14x + 7
GCF___
List factors of ___
4) 2x2 + 18x + 40
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
5) 3x2 - 15x + 12
GCF___
List factors of ___
7) 3x2 - 24x + 36
GCF___
List factors of ___
May 04, 2016
6) 2x2 - 22x + 48
GCF___
List factors of ___
8) 5m2 - 5m - 30
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
9) 2c2 - 4c - 16
GCF___
List factors of ___
11) ax2 + 3ax + 2a
GCF___
List factors of ___
May 04, 2016
10) 2x2 - 2x - 144
GCF___
List factors of ___
12) x3 + 7x2 + 10x
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
13) ax2 - 3ax + 2a
GCF___
List factors of ___
15) 3x3 - 6x2 - 24x
GCF___
List factors of ___
May 04, 2016
14) 2ax2 - 2ax - 12a
GCF___
List factors of ___
16) 3x2 - 6x - 24
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
17) 7ax2 - 14ax + 7a
GCF___
List factors of ___
19) 4x2 + 8x + 4
GCF___
List factors of ___
May 04, 2016
18) x2y + 8xy + 12y
GCF___
List factors of ___
5­4­16 Alg L Day 3 ­ Factor Completely.notebook
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May 04, 2016