2.3 Factoring Polynomials Math Worksheet Page 5
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7• If a polynomial has more than three terms, you may be able to factor it by
grouping. This is only possible if the grouping of terms allows you to divide out
the same common factor from each group.
Need to Know
• To factor a polynomial fully means that only 1 and 21 remain as common factors
in the factored expression.
• To factor polynomials fully, you can use factoring strategies that include
dividing by the greatest common factor (GCF)
•
2
recognizing a factorable trinomial of the form
ax
1 bx 1 c,
where
a 5 1
•
2
recognizing a factorable trinomial of the form
ax
1 bx 1 c,
where
a 2 1
•
recognizing a polynomial that can be factored as a difference of squares:
•
2
2
a
2 b
5 (a 1 b) (a 2 b)
recognizing a polynomial that can be factored as a perfect square:
•
2
2
2
2
2
2
a
1 2ab 1 b
5 (a 1 b)
and
a
2 2ab 1 b
5 (a 2 b)
factoring by grouping
•
CHECK Your Understanding
Factor.
1.
2
2
x
2 6x 2 27
4x
1 20x 1 25
a)
c)
2
2
b)
25x
2 49
d)
6x
2 x 2 2
Each expression given can be factored by grouping. Describe how you would
2.
group the terms to factor each.
ac 1 bc 2 ad 2 bd
a)
2
2
b)
x
1 2x 1 1 2 y
2
2
c)
x
2 y
2 10y 2 25
Factor.
3.
2
2
x
2 3x 2 28
9x
2 42x 1 49
a)
c)
2
2
b)
36x
2 25
d)
2x
2 7x 2 15
PRACTISING
Factor.
4.
3
2
4x
2 6x
1 2x
a)
3
2
2
4
3
b)
3x
y
2 9x
y
1 3xy
4a(a 1 1) 2 3(a 1 1)
c)
2
7x
(x 1 1) 2 x(x 1 1) 1 6(x 1 1)
d)
e)
5x(2 2 x) 1 4x(2x 2 5) 2 (3x 2 4)
2
2
4t(t
1 4t 1 2) 2 2t(3t
2 6t 1 17)
f )
Factor.
5.
2
2
x
2 5x 2 14
2y
1 5y 2 7
a)
d)
2
2
2
2
b)
x
1 4xy 2 5y
e)
8a
2 2ab 2 21b
2
2
c)
6m
2 90m 1 324
f ) 16x
1 76x 1 90
102
2.3 Factoring Polynomials
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