2.3 Factoring Polynomials Math Worksheet Page 6
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1
2
3
4
5
6
7Factor.
6.
2
2
x
2 9
9( y 2 1)
2 25
a)
d)
2
2
2
4n
2 49
3x
2 27(2 2 x)
b)
e)
8
2
2
x
2 1
q
1 81
c)
f )
2p
Factor.
7.
2
a)
ax 1 ay 1 bx 1 by
d)
1 2 x
1 6x 2 9
2
2
2ab 1 2a 2 3b 2 3
a
2 b
1 25 1 10a
b)
e)
3
2
2
2
x
1 x
2 x 2 1
2m
1 10m 1 10n 2 2n
c)
f )
Andrij claims that the following statement is true:
8.
3
3
2
2
K
x
2 y
5 (x 2 y) (x
1 y
)
Is Andrij correct? Justify your decision.
Factor.
9.
2
2
2x(x 2 3) 1 7(3 2 x)
y
2 49 1 14x 2 x
a)
d)
2
b)
xy 1 6x 1 5y 1 30
e)
6x
2 21x 2 12x 1 42
3
2
3
2
x
2 x
2 4x 1 4
12m
2 14m
2 30m 1 35
c)
f )
3
2
Show that the function
f (n) 5 2n
1 n
1 6n 1 3
always produces a
10.
T
number that is divisible by an odd number greater than 1, for any natural
number, n.
Sedna has designed a fishpond in the shape of a right triangle with two sides
11.
of length a and b and hypotenuse of length c.
2
a) Write an expression in factored form for a
.
b) The hypotenuse is 3 m longer than b, and the sum of the lengths of the
hypotenuse and b is 11 m. What are the lengths of the sides of the pond?
Saturn is the ringed planet most people think of, but Uranus and Neptune
12.
A
also have rings. In addition, there are ringed planets outside our solar
system. Consider the cross-section of the ringed planet shown.
outer ring
inner ring
planet
r
1
r
2
r
3
a) Write factored expressions for
i)
the area of the region between the planet and the inner ring
ii) the area of the region between the planet and the outer ring
iii) the difference of the areas from parts (i) and (ii)
b) What does the quantity in part (iii) represent?
Chapter 2 Equivalent Algebraic Expressions
103
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