Quadratics Jeopardy

Common Factor

100

Factorise:

2x+8

2(x+4)

200

Factorise:

2x²+3x

x(2x+3)

300

Solve:

2x²-12=0

x=± √6

400

Solve:

9x²-3x=0

3x(3x-1)=0

 x=0 or x=  1/3

500

Solve

8x²=16

8x²-16=0

8(x²-2)=0 

x= ± √2

DOPS

100

Factorise

x²-16

(x+4)(x-4)

200

Factorise

25x²-64

(5x+8)(5x-8)

300

Factorise: 36a²-9b²

(6a+3b)(6a-3b)

400

Solve 2a²-14=0

2(a²-7)

=2(a+√7)(a-√7)

a=±√7

500

Solve: 3x²=27

3(x²-9)=0

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

x=± 3

Monic Trinomials

100

Factorise: x²+4x-12

(x-2)(x+6)

200

Factorise: x²-12x-32

(x-8)(x-4)

300

Factorise: 3x²-24x+48

3(x²-8x+16)

=3(x-4)(x-4)

=3(x-4)²

400

Solve: x²+2x-15=0

(x-3)(x+5)=0

x=3 or x=-5

500

Solve:

2x²-10x-48=0

2(x²-5x-24)=0

2(x-8)(x+3)=0

x=8 or x=-3

Completing the Square

100

Factorise, if possible:

x²+4x-1

(x+2)²-5

= (x+2+√5)(x+2-√5)

200

Factorise, if possible:

x²-2x-7

(x-1)²-8

= (x-1+√8)(x-1-√8)

300

Factorise, if possible:

x²-6x+15

(x+3)²+6

Therefore, not possible

400

Factorise, if possible:

x²-12x+15

(x-6)²-21

= (x-2+√21)(x-6-√21)

500

Factorise, fully simplifying the surd:

x²-3x+5

(x-3/2)²- 29/4

= (x-3/2+√(29/4))(x-3/2-√(29/4))

= (x-(3-√29)/2)(x-(3+√29)/2)

Mixed

100

Factorise:

2r² s-8rs²

2rs(r-4s)

200

Factorise: 81t²-4s²

(9t+2s)(9t-2s)

300

Solve:

49a²-3=0

(7a+√3)(7a-√3)=0

a=±√3/7

400

Factorise:

3x^2+2x+9x+6

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

=(3x+2)(x+3)

500

Solve:

3a²-24a+48=0

3(a²-8a+16)=0

3(a-4)²= 0

a = 4