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Would you like to know how the 2005 HSC exams were marked? HSC and SC 2005: Feedback and Advice Saturday 25th February, 2006 Macquarie University – Mason Theatre Free for MANSW members $20 for non-members Program <TABLE cellSpacing=0 cellPadding=5 border=0><TBODY><TR><TD>8:45am...

Yes. That's right. If it's different, a mistake has been made. Students should check their solutions as well as just doing them.

You forgot the remainder. It should be A(x).Q(x)+R, for some number R. If it is a more general divisor, A(x).Q(x)+R(x) where deg(R(x)) < deg(A(x)). The inspection method works for these as well. Just use the last term in Q(x) to get R(x). Also, in your example, I would suggest...

I noticed last night Timbk2 changed the name of the BOS wiki to Biki. That's a funny one! lol.

I can be used for quadratic divisors as well: http://www.purplemath.com/modules/synthetic-division-sgnd.pdf

Ask them at your own risk. Most maths teachers don't know much about maths. Ha! Ha! And I bet most of them would not be capable of proving the formula for the square roots of a complex number. Neverthless, here's the MUCH LONGER SOLUTION...

It's called synthetic division. http://www.purplemath.com/modules/synthdiv.htm http://www.purplemath.com/modules/synthdiv2.htm

No. x<SUP>4</SUP>-16x<SUP>2</SUP>-15<SUP>2</SUP>=0. This part is right!

You can just use the formula and do it in 1 line without mucking about with equations.

You missed the square (which I made red): x⁴-16x²-15²=0.

It's not hard to derive. Square both sides: Or alternatively just follow what pLuvia and Riviet said, but in the general case (a bit longer, but it still works).

My solution to the Coroneos question used 2 formulae simultaneously. Square roots of a complex number, and quadratic formula. You don't have to use the quadratic formula to solve a quadratic, but it's easier in your example if you do. Likewise, you don't have to use the formula for the...

It is in the syllabus. sgn(b) is the sign of b. So if b > 0, sgn(b)=+1, if b < 0, sgn(b)=-1. If b=0, sgn(b)=0, but then there's no need for the formula. Using this formula is a much faster method and so as far as risk is concerned, there's much less chance of making a mistake if you...

It's easier if you use the formula:

In my solution, w=16-30i.