 Hello and welcome to another problem-solving session on factor theorem. The question says show that x-3 is a factor of fx x cube minus 3x square plus 4x minus 12 It's a very easy question. The solution lies in Application of factor theorem. What is factor theorem guys if ax plus b is a factor of of fx Right, then where fx is a polynomial then F of minus b by a is 0. This is what is factor theorem Right, or the otherwise otherwise is that means if f of minus b by a is 0 by Cversa that is if F of minus b by a is 0 then ax plus b is a factor of fx Correct. This is what we learned in factor theorem. Now. Let's take this particular example It says check whether x-3 is a factor, right? So let's check f of 3 first f of 3 y f of 3 so again in all these Sessions, we have been describing this particular process. So your ax plus b is x minus 3 in this case So clearly a is 1 and b is minus 3. So minus b by a which is required here is 3 So you have to check for f of 3. So f of 3. Let's put the values 3 to the power 3 minus 3 times 3 squared that is how you deploy the value of x in place of x Correct. So what is this value? This is 27 guys minus 27 Plus 12 minus 12, which is very clearly 0 Since it is 0 Since and we write since f 3 is 0 Is 0 or rather don't write the word 0 write the numeral 0 Because the word 0 means something else which we discussed 0 of a polynomial So f of 3 is 0 then Since or rather since it was since hence you will write hence or therefore x minus 3 is a factor of FX which is given as What was the fact, you know expression and it was I think yeah, so let's check x cube minus, okay So it's nothing but the effect FX is how much x cube minus 3 x squared Plus 4x minus 2 right of this particular polynomial x minus 3 is a factor