Factorising- Term 2

Question 1

Factorise 8x+20

Answer 1

Look for HCF. HCF goes outside the brackets.
How many times does 4 go into 8x?
How many times does 4 go into 20?

4(2x+5)

Question 2

Factorise 15y - 10a+5

Answer 2

5(3y-2a+1)

Question 3

Factorise 6a+3ab

Answer 3

3a(2+b)

Question 4

Factorise 18a^2b-24ab

Answer 4

6ab(3a-4)

Question 5

Factorise

X^2+8x+15

Answer 5

5+3=8
5x3=15

(X+3)(X+5)

Question 6

Factorise

X^2+10x+24

Answer 6

(X+4)(X+6)

Question 7

Factorise

X^2+2x-15

Answer 7

(X-3)(x+5)

Question 8

Factorise

X^2-7x+12

Answer 8

(X-3)(x-4)

Question 9

Factorise

2x^2-11x+12

Answer 9

Smiley face method
-3x-4=12
-8+-3=-11
(2x-3)(x-4)
\.     \  /    /
  \.         /
    \.     /

Question 10

Factorise

3x^2-7x-6

Answer 10

Smiley face

3x+2)(x-3

Question 11

What is the rule for factorising two squares?

Answer 11

a^2-b^2= (a-b)(a+b)

Question 12

Factorise x^2-16

Answer 12

15 is a square number
Rule: a^2-b^2= (a-b)(a+b)

=x^2-4^2
=(x-4)(X+4)

Question 13

Factorise

X^2-100

Answer 13

100 is a square number
Rule: a^2-b^2= (a-b)(a+b)

X^2-10^2
(X-10)(x+10)

Question 14

Factorise

9y^2-25

Answer 14

25 is a square number
Rule: a^2-b^2= (a-b)(a+b)
=(3y)^2-5^2

Just 3y^2 would cause only the y to be squared, brackets make it all of it

Question 15

Factorise

9-x^2

Answer 15

=3^2-x^2

=(3-x)(3+X)

Question 16

Factorise 3(x+4)+2x(x+4)

Answer 16

(X+4)(3+2x)

Question 17

Factorise 4(x+1)^2+3x(x+1)

Answer 17

(Only the (x+1) is squared)
=(x+1)(4(x+1)+3x)
=(x+1)(4x+4+3x)
=(x+1)(7x+4)

Question 18

Factorise 2(x+3)^3+3x(x+3)^2

Answer 18

=(x+3)^2`(2(x+3)+3x)
(X+3)^2(2x+6+3x)
(X+3)^2(5x+6)