Quadratic Expressions Worksheets Page 13
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36number and algebra
− 17x + 7
− 13x − 14
− 9x − 9
2
2
2
6x
12x
10x
g
h
i
+ 3x − 2
+ 5x − 2
+ x − 2
2
2
2
20x
12x
15x
j
k
l
Factorise each of the following, remembering to look for a common factor first.
7
2
+ 2x − 6
2
− 60x − 21
2
+ 12x − 12
4x
9x
72x
a
b
c
−18x
+ 3x + 3
−60x
+ 150x + 90
+ 18ax − 105a
2
2
2
24ax
d
e
f
−8x
+ 22x − 12
−10x
+ 31x + 14
−24x
+ 35x − 4
2
2
2
g
h
i
−12x
− 2xy + 2y
−30x
+ 85xy + 70y
−600x
− 780xy − 252y
2
2
2
2
2
2
j
k
l
underSTandIng
Consider the expression (x − 1)
+ 5(x − 1) − 6.
2
8
Substitute w = x − 1 in this expression.
a
Factorise the resulting quadratic.
b
Replace w with x − 1 and simplify each factor. This is the factorised form of the
c
original expression.
Use the method outlined in question
to factorise each of the following expressions.
9
8
(x + 1)
+ 3(x + 1) − 4
(x + 2)
+ (x + 2) − 6
2
2
a
b
(x − 3)
+ 4(x − 3) + 4
(x + 3)
+ 8(x + 3) + 12
2
2
c
d
(x − 7)
− 7(x − 7) − 8
(x − 5)
− 3(x − 5) − 10
2
2
e
f
+ x − 0.75.
2
Factorise x
10
Students decide to make Valentine’s Day cards. The total area of each card is equal to
11
2
− 4x − 5) cm
2
(x
.
Factorise the expression to find the dimensions of the cards in
a
terms of x.
Write down the length of the shorter side in terms of x.
b
If the shorter sides of a card are 10 cm in length and the longer
c
sides are 16 cm in length, find the value of x.
Find the area of the card proposed in part
.
d
c
Happy
If the students want to make 3000 Valentine’s Day cards, how
e
Valentine’s
much cardboard will be required? Give your answer in terms of x.
Day
The area of a rectangular playground is given by the general
12
+ 11x + 3) m
2
2
expression (6x
where x is a positive whole number.
Find the length and width of the playground in terms of x.
a
Write an expression for the perimeter of the playground.
b
If the perimeter of a particular playground is 88 metres, find x.
c
reaSOnIng
Cameron wants to build an in‐ground
13
‘endless’ pool. Basic models have a
depth of 2 metres and a length triple
the width. A spa will also be attached
to the end of the pool.
The pool needs to be tiled. Write
a
an expression for the surface area
of the empty pool (that is, the
floor and walls only).
Maths Quest 10 + 10A
280
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