Expanding expressions
-3(x - 5)
= -3x + 15
x2 + 11x + 18
= (x + 9) (x + 2)
3x2 + 10x + 3
= 3x2 + x + 9x + 3
= 3x(x+1) + 3(x+1)
= (x+1) (3x+3)
What has hands but can't clap?
A clock
How many children do I have?
2
(x + 5) (x + 4)
= x2 + 4x + 5x + 20
= x2 + 9x +20
x2 - 8x + 16
= (x - 4) (x - 4)
= (x - 4)2
9x2 + 6x - 8
= 9x2 + 12x - 6x - 8
= 3x(3x+4) - 2(3x+4)
= (3x+4) (3x-2)
What has a thumb and four fingers but is not a hand?
How many years has Miss Karen been a Teachers Aide?
20 years
(2x - 1) (3x + 5)
= 6x2 + 10x - 3x - 5
= 6x2 + 7x - 5
2x2 - 10x - 28
= 2(x2 - 5x - 14)
= 2(x - 7)(x + 2)
8x2 - 20x + 8
= 8x2 - 16x - 4x + 8
= 8x(x - 2) -4(x - 2)
= (8x-4) + (x-2)
A man who was outside in the rain without an umbrella or hat didn't get a single hair on his head wet. How did he do it?
He was bald.
Where did I grow up?
Sydney
(x - 4)2
= x2 - 8x + 16
x2 - 3x - 54
= (x - 9)(x + 6)
6x2 + 38x + 40
= 2 (3x2 + 19x + 20)
= 2 (3x2 + 15x + 4x + 20)
= 2 [ 3x(x+5) + 4(x+5) ]
= 2 (x+5) (3x+4)
What question can you never answer 'Yes' to?
Are you asleep yet?
How old am I?
50
(x + 2)(x + 4) - (x - 2)(x - 5)
= (x2 + 4x + 2x + 8) - (x2 - 5x - 2x + 10)
= (x2 + 6x + 8) - (x2 - 7x + 10)
= x2 + 6x + 8 - x2 + 7x - 19
= 13x - 2
The product of two consecutive, even positive numbers is 168.
USE A QUADRATIC EQUATION to find the two numbers.
x(x + 2) = 168
x2 + 2x - 168 = 0
(x + 14)(x - 12) = 0
x = -14 or x = 12
The two numbers are 12 and 14.
Solve 10x2 - 13x - 3 = 0
10x2 - 15x + 2x - 3 = 0
5x(2x-3) + (2x-3) = 0
(2x-3) (5x+1) = 0
2x-3 = 0 therefore x = 3/2
5x+1 = 0 therefore x = -1/5
Forward I am heavy, but backward I am not. What am I?
The word 'ton'
Which date is Miss Karen's birthday? Closest answer gets the points.
24 August 1966
Bonus points if you can work out how old she is?