Variation 3 · answer guide

Polynomial graphs — Simple vs double root

Question

Which polynomial matches “monic quartic, double zero at , divisible by ”?

This practice question was inspired by Question 5 in the 2020 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: use degree, leading coefficient, root multiplicities and any forced factors to decide shape. is monic of degree .
Simplify the previous line carefully, keeping exact values where possible.It has double zero at and the required quadratic factor.
Finish the calculation, then check that the result meets the question’s conditions.Option C is not monic (leading coefficient ); B is cubic; D lacks the quadratic factor.
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Degree and leading coefficient check eliminate B–D.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.