Here are summary for polynomials (factor, remainder theorem, and solving cubic equations):
For a polynomial P(x), when P(x) is divided by (x -b), the remainder is P(b).
For a polynomial P(x), if (x-b) is a factor of P(x), then P(b) = 0 (since remainder = 0).
Solving cubic equations (for O Level Additional Mathematics):
The O level method of solving cubic equation involves transforming the cubic equation ax3 + bx2 + cx + d =0 in (x- g)(x-h)(x-f) = 0. Then the solutions of x are g, h and f.
In O Level Additional Mathematics, students are required to decompose a fraction with denominator of (ax+b)(cx+d) or (ax+b)2(cx+d) or (ax+b)(cx2+d) into partial fractions.
To do so, students need to first make the fraction into proper fractions, then find the unknowns based on identities.
Want to learn more about Polynomials and Partial Fractions for O Level Add Maths?
Polynomials and partial fractions are relatively easy topics for O Level Additional Mathematics. Once you master the steps to solve the questions, you will be able to do the exam questions with ease.
In my course on polynomial and partial fractions, I go into detail not only the concepts but how to apply them in different scenarios. We will go through many exam questions together step-by-step so that students finish the course equipped with the skills needed to tackle their test and exam questions on polynomials and partial fractions with confidence. You can purchase the course instantly on Udemy, and watch and learn instantly. You can find my complete on Polynomials and Partial Fractions here.