Quadratics!!

Factorising (single bracket)

100

Factorise the following (put it back into brackets):

x² + 3x

x(x + 3)

200

Factorise the following (put it back into brackets):

x² - 10x

x(x - 10)

300

Factorise the following (what do they both have in common?):

2x² + 12

2(x + 6)

400

Factorise the following (what do they both have in common?):

10x² + 10x

10x(x + 1)

500

Factorise the following (what do they both have in common?):

10x² - 120

10(x² - 12)

Factorising (double brackets)

100

Factorise the following:

x² + 3x + 2

(x + 2)(x + 1)

200

Factorise the following:

x² + 5x + 6

(x + 2)(x + 3)

300

Factorise the following:

x² - 5x + 6

(x - 3)(x - 2)

400

Factorise the following:

x² - 10x + 25

(x - 5)(x - 5)       OR       (x - 5)²

500

Factorise the following (first take out a common factor):

2x² + 6x + 4

Step 1:  2(x² + 3x + 2)

Step 2:  2(x + 2)(x + 1)

Expanding (single bracket)

100

Expand the following:

x(x + 5)

x² + 5x

200

Expand the following:

2(x - 10)

2x - 20

300

Expand the following:

x(2x - 3)

2x² - 3x

400

Expand the following:

5x(x - 3)

5x² - 15x

500

Expand the following:

(x + 4)²

(x + 3)(x + 3) = x² + 6x + 9

Expanding (double brackets)

100

Expand the following:

(x + 1)(x + 5)

x² + 6x + 5

200

Expand the following:

(x + 3)(x + 10)

x² + 13x + 30

300

Expand the following:

(2x + 1)(x + 5)

2x² + 11x + 5

400

Expand the following:

(x - 4)(x + 4)

x² - 16

500

Expand the following:

(x - 10)(x + 10)

x² - 100

Null Factor Law

100

What are the solutions to x in:

(x - 3)(x - 10)

x = 3 and 10

200

What are the solutions to x in:

(x + 5)(x + 6)

x = -5 and -6

300

What are the solutions of x in:

x(x + 24)

x = 0 and -24

400

What are the solutions of x in:

2x(x - 10)

x = 0 and 10

500

What are the solutions to x in:

x² - 100

(HINT: Factorise first!)

Step 1: (x + 10)(x - 10)

Step 2: x = 10 and -10