Factorising and Expanding

Question 1

Expand with FOIL

(x+3)(x+4)

Answer 1

x^2 + 7x + 12

Question 2

Factorise with DOPS

a^2 - b^2

Cannot be done with addition

Answer 2

(a+b)(a-b)

Question 3

Factorising perfect squares

a^2 + b^2

Answer 3

(a+b)^2

Question 4

Factorise by taking out common factors

-3x - 12

Answer 4

-3(x+4)

Question 5

Factorise with DOPS after taking out a common factor

12y^2 - 1200

Answer 5

12(y+10)(y-10)

Question 6

Factorise using DOPS and surds

x^2 - 10

Answer 6

(x-√10)(x+√10)

Question 7

Factorise by grouping

x^2-x+ax-a

Answer 7

x(x-1) + a(x-1)
= (x-1)(x+a)

Question 8

Factorise the monic

x^2 + 8x + 15

Answer 8

x 5
x 3
=(x+3)(x+5)

Question 9

Factorise the non-monic

6^x + 19x +10

Answer 9

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

Question 10

Factorise the monic by first taking out a common factor

2x^2 - 10x - 28

Answer 10

2(x^2 - 5x - 14)
x -7
x 2
=(x+2)(x-7)

Question 11

Factorise by completing the square

x^2 + 8x - 3

Answer 11

x^2 + 16 + 8x -16 - 3
(x+4) - 19
(x + 4 - √19)(x + 4 + √19)

Half the coefficient and then square it

Question 12

Factorise using null factor law

p x q = 0

Answer 12

0 = p or q

Question 13

The quadratic formula

Answer 13

(-b ± √b^2 - 4ac)/2

Question 14

The Discriminant

Answer 14

△ = b^2 - 4ac

Question 15

Numbe of solutions for the discriminant

Answer 15

△ < 0 there are 0 real solutions
△ = 0 there is 1 real solution
△ > 0 there are 2 real solutions