Factorising & Solving monic & non-monic quadratics

Expanding expressions

100

-3(x - 5)

= -3x + 15

200

(x + 5) (x + 4)

= x² + 4x + 5x + 20

= x² + 9x +20

300

(2x - 1) (3x + 5)

= 6x² + 10x - 3x - 5

= 6x² + 7x - 5

400

(x - 4)²

= x² - 8x + 16

500

(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

Factorising monic quadratic

100

x² - 5x + 6

= (x - 3) (x - 2)

200

x² - 8x + 16

= (x - 4) (x - 4)

= (x - 4)²

300

2x² - 10x - 28

= 2(x² - 5x - 14)

= 2(x - 7)(x + 2)

400

x² - 3x - 54

= (x - 9)(x + 6)

500

x^2-13x+36

(x-9)(x-4)

Factorising non-monic quadratic

100

3x² + 10x + 3

= 3x² + x + 9x + 3

= 3x(x+1) + 3(x+1)

= (x+1) (3x+3)

200

9x² + 6x - 8

= 9x² + 12x - 6x - 8

= 3x(3x+4) - 2(3x+4)

= (3x+4) (3x-2)

300

6x² + 38x + 40

= 2 (3x² + 19x + 20)

= 2 (3x² + 15x + 4x + 20)

= 2 [ 3x(x+5) + 4(x+5) ]

= 2 (x+5) (3x+4)

400

9x² - 4

(3x+2) (3x-2)

500

10x² - 13x - 3 

(2x-3) (5x+1) 

Solve for x

100

Solve for x, 

(x+4)(x-2)=0

x=-4, x=2

200

Solve for x,

(2x+4)(x-3)=0

 

x=-2, x=3

300

Solve for x, 

x^2+6x+8=0

x=-2, x=-4

400

Solve for x, 

2x^2-10x+12=0

x=2, x=3

500

Solve for x, 

4x^2-4x-3=0

x=3/2, x=-1/2

Riddles

100

What has hands but can't clap?

A clock

200

What has a thumb and four fingers but is not a hand?

A glove

300

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.

400

What question can you never answer 'Yes' to?

Are you asleep yet?

500

Forward I am heavy, but backward I am not. What am I?

The word 'ton'