Core 4 - Simplifying Cubics

Question 1

What is the method for dividing a polynomial by a smaller/equal power by inspection?

Answer 1

Set up two brackets, with a known factor, and a quadratic. Work out the exponential co-efficient.

Then work out the last term by multiplying the last term of the first bracket by something to give the last term in the overall equation.

Then decide which term is easier to work out from the x^2 term or the x term (normally smaller exponential). There are two parts to add to make this term. Make sure they add to make one of the terms, and double check that it works for the other.

Question 2

What is the method for dividing a polynomial by a quadratic using the DMS method?

Answer 2

Set up the division, including any 0 terms for missing parts to make sure terms are added to the correct columns later. Start by dividing the right hand term of the denominator by the largest term of the polynomial. This should be placed in the appropriate column for the x exponential