Factorise 45x^2 - 46x + 8

The way to do this is if the equtation is in

ax^2+bx+c form

then multiply a and c together and get

a times c=y times z where y+z=b then make the form into

ax^2+yx+zx+c so

a=45

b=-46

c=8

a time c=45 times 8=360

then find what 2 numbers add up to - 48 and multiply to get 360

the numbers must be both negative because only same signs multiplied by each other can result in a positive number

factor 360

360,1

180,2

120,3

90,4

72,5

60,6

45,8

40,9

36,10

30,12

24,15

20,18

now add and find which add up to 48

360+1=361

180+2=182

120+3=123

90+4=94

72+5=77

60+6=66

45+8=53

40+9=49

36+10=46 match

30+12=42

24+15=39

20+18=38

the numbers are - 36 and - 10

split it up

45x^2-10x-36x+8

group

(45x^2-10x) + (-36x+8)

factor out the common factors

(5x) (9x-2) + (-4) (9x-2)

reverse distributive property which is ab+ac=a (b+c)

(5x-4) (9x-2)

tada, it's factored

factored form is (5x-4) (9x-2)