Mathematics | Course : Model Mathematics III (Integrated Pathway)
Domain - The Complex Number System
Cluster - Use complex numbers in polynomial identities and equations.
[MIII.N-CN.C.9] - (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
- Fundamental Theorem of Algebra
The theorem that establishes that, using complex numbers, all polynomials can be factored into a product of linear terms. A generalization of the theorem asserts that any polynomial of degree n has exactly n zeros, counting multiplicity. - Quadratic polynomial
A polynomial where the highest degree of any of its terms is 2.
[MII.A-REI.B.4.b] -
Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
[MIII.A-APR.B.2] -
Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).