2.3 Factoring Polynomials Math Worksheet Page 2
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72
Selecting a factoring strategy: Grouping
EXAMPLE
3
2
Factor
f (n) 5 n
1 3n
1 2n 1 6
by grouping.
Noah’s Solution
3
2
I separated
f(n)
into two groups:
f (n) 5 n
1 3n
1 2n 1 6
the first two terms and the last two
3
2
5 (n
1 3n
) 1 (2n 1 6)
terms.
I factored each group by dividing
2
n
(n 1 3) 1 2(n 1 3)
5
by its common factor.
Then I factored by dividing each term
2
1 2)
5 (n 1 3)
(n
by the common factor n 1 3.
Both factors produce numbers greater
than 1, so
f (n)
can never be expressed
as the product of 1 and itself. So Mai’s
claim is true.
Reflecting
A.
Why is Noah’s method called factoring by grouping?
B.
What are the advantages and disadvantages of Sally’s and Noah’s methods
of factoring?
APPLY the Math
3
Selecting factoring strategies: Quadratic
EXAMPLE
expressions
Factor.
2
2
x
2 x 2 30
9x
1 30x 1 25
a)
d)
2
2
b)
18x
2 50
e)
2x
1 x 1 3
2
10x
2 x 2 3
c)
Winnie’s Solution
This is a trinomial of the form
2
a)
x
2 x 2 30
2
ax
1 bx 1 c,
where
a 5 1.
I can
5 (x 1 5) (x 2 6)
factor it by finding two numbers
whose sum is 21 and whose
product is 230. These numbers are
5 and 26.
Chapter 2 Equivalent Algebraic Expressions
99
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