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)