Name the type of factoring (DoPS, GCF, Trinomials, factoring by parts, factoring with a leading coefficient)

1) (x - 9)(x + 2)  ==> trinomials

2) (s + z) (3m - 2n)  ==> factorising by parts

3) (x + 2)(5x + 3)  ==> factorising with a leading coefficient

4) 9y²(3y² - 2)  ==> GCF

5) (4m - 12)(4m + 12)  ==> DoPS

Step-by-step explanation:

1). Find multiples of -18 that add up to -7

Multiples of -18 : (only one number can be negative, because positive*negative = negative)

1, 18 or 3, 6 or 2, 9

Only one pair adds up to -7 which is -9 + 2

Hence ==> (x - 9)(x + 2)

2). Find the common things between the terms and factorise it out  

3m(s + z) - 2n(s + z)

Since the terms inside the brackets are the same, you simplify it to:

(s + z) (3m - 2n)

3). Multiply the first coefficient with the last coefficient: 5(6) = 30

Find two numbers that multiply to 30 and add up to the middle coefficient -13.

Multiples of 30 are: 1, 30 or 2, 15 or 3, 10 or 5,6, but only one pair would add to -13 and that is 3 and 10

So the next step is to write it in this form: 5x² + 10x + 3x + 6

Factorise: 5x(x + 2) + 3(x + 2)

(x + 2)(5x + 3)

4). Find the greatest common factor within 27y⁴ and 18y², which is 9y²

9y²(3y² - 2)

5). Square root each number: √16 = 4 and √144 = 12

(4m - 12)(4m + 12)