Here are summary for polynomials (factor, remainder theorem, and solving cubic equations):

## Remainder Theorem:

For a polynomial P(*x*), when P(*x*) is divided by (*x* -b), the remainder is P(b).

## Factor Theorem:

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 ax^{3} + bx^{2} + cx + d =0 in (x- g)(x-h)(x-f) = 0. Then the solutions of x are *g*, *h* and *f*.

Partial Fractions

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)(cx^{2}+d) into partial fractions.

To do so, students need to first make the fraction into proper fractions, then find the unknowns based on identities.

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