Polynomials Made Easy: Master Simultaneous Equations in Secondary Additional Math

Polynomials are a key topic in Secondary Additional Math, and many students find them challenging. Take this classic question:

The polynomial ax² + bx + 2, where a and b are constants, is divisible by x−1. When it is divided by x+2, the remainder is 24. Find the values of a and b.

Though it may seem straightforward, it requires careful steps to solve. This question involves forming simultaneous equations from the given information. Students often make mistakes when evaluating polynomials at specific values, so accuracy in the first step is crucial.

Start by applying the Remainder Factor Theorem. Because the polynomial is divisible by x−1, substituting x=1 gives the first equation. Similarly, substituting x=−2 provides the second equation using the remainder 24. Once these two equations are correctly formed, a self-motivated learner can solve them using substitution or elimination.

Solving these simultaneous equations reveals the values of a and b, giving a confident understanding of polynomials. With this approach, even challenging Add Math questions become manageable.

For students aiming to be confident learners, practising such problems strengthens problem-solving skills and builds mastery in Secondary math. For those who need guidance, Superstar Teacher offers instant homework help and on-demand homework help to ensure every question is fully understood.

If forming the equations or solving them feels tricky, scroll down to see the detailed step-by-step discussion between a mentor and student, showing exactly how to tackle this Additional Math polynomials question.