Factorise the quadratic expression fully: x2 + 7x + 10
(1)
2
Factorise: x2 + 3x - 10
(1)
3
Factorise: x2 - 9x + 18
(1)
4
Factorise fully: x2 + 11x + 24
(2)
5
Factorise fully: x2 - 2x - 15
(2)
6
Multiply out (x + 9)(x - 4) and then factorise your answer to show you get back the original factors.
(2)
7
Factorise the difference of two squares: x2 - 16
(1)
8
Factorise fully: 9x2 - 100
(2)
9
Factorise x2 + 8x + 7 and use the factorised form to solve x2 + 8x + 7 = 0
(3)
10
Factorise x2 + 14x + 45 and hence find the values of x for which the expression equals zero.
(3)
11
Factorise fully and solve x2 - 4x - 45 = 0
(3)
12
Factorise fully: 25x2 - 64
(1)
13
Expand (x + 6)(x - 2) to form a quadratic. Then find all values of x such that this quadratic equals 9.
(3)
14
Factorise x2 + 17x + 72 fully and state the roots of the quadratic equation x2 + 17x + 72 = 0.
(3)
15
The product of two consecutive integers is 90. Let the smaller integer be x. Write an equation in x and solve it to find the positive value of x.
(3)
16
Given that f(x) = x2 + 19x + 90: (a) factorise f(x) fully (b) find f(-12).
(3)
17
Show that x2 + 10x + 25 can be written as (x + 5)2. Use this to explain why x2 + 10x + 25 is never negative for any real x. Give the value(s) of x for which the expression equals 0.