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.
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