State and motivate the Remainder Theorem with examples and analogy to integers. Statement and proof of the Factor Theorem. Factorisation of ax^2 + bx + c, a ≠ 0 where a, b, c are real numbers, and of cubic polynomials using the Factor Theorem.
9.A.P.3
Recall of algebraic expressions and identities. Further identities of the type: (x + y + z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2zx, (x ± y)^ 3 = x^3 ± y^3 ± 3xy (x ± y), x^3 + y^3 + z^3 – 3xyz = (x + y + z) (x^2 + y^2 + z^2 – xy – yz – zx) and their use in factorization of polynomials. Simple expressions reducible to these polynomials.
