Answer:
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)
