TYS: Believe you've already heard of the fabled The 阴阳眼 Of Plane Geometry?

Welcome to Jφss Sticks Subtraction!

Like the The Cover-Up Rule, Synthetic Division isn't officially taught in all schools and are not covered by most textbooks here.

Technically, it should not be a problem if you run amok and use this method rampantly in your exams, but you'll also run a slight risk of your examiner/marker getting startled or even slightly annoyed (yeah sad but true) by those 'pagan' workings on your script (especially if it's not officially taught at your school).

So always, always cover yourself by writing a BIG "Using Synthetic Division," ... at the start of your working!

Those who're interested in this method will find the following video useful:

While we'll all agree that this is really a handy method especially when used to check your answer, an old-school Miss Loi would still advocate that you make sure you get your foundations right first before running riot with it.

P.S. This should be less of an issue at A Level (if that's what you're asking) but nevertheless it's always good practice to declare your method before every major chunk of your hieroglyphic workings to make it easier for your marker to follow (after all, marking ain't a relaxing job) - so that you'll still give him/her a reason to award method marks if you've made a careless mistake.

Is this method allowed in A level?

Following the extended definition of the Factor Theorem in comment #4, we can similarly generalize the Remainder Theorem to this:

This being last-minute notes for last-minute students, Miss Loi didn't state it this way so as to minimize any confusion with most textbooks (which only state the case for (x-a)) - though you're expected to know how to find the remainder when f(x) is divided by (ax-b)

That's why Miss Loi has specially included part iii. (as a reminder) in the example question in A.

Happy Birthday!

Someone: Are you referring to the extended definition of the Factor Theorem?

i.e.

For this case, Miss Loi didn't state this as it's rare in O-Level solution of cubic equation questions where the first factor (see step C1 above) is a fraction i.e. substituting a b/a value into f(x) for your trial and error.

HOWEVER we can't rule out such a root appearing in the remaining quadratic equation (see step C2 above) but you should be able to find it easily either via the via quick Trial and Error method (described in B above) or the quadratic formula.

Haha, I enjoyed your sergent loi's series It's very cute and enlightening. Sorry for not visiting your blog these days, busy like mad dog, as you should know

Have fun teaching!