Mathematics | Course : Model Algebra II (Traditional Pathway)
Domain - The Complex Number System
Cluster - Use complex numbers in polynomial identities and equations.
[AII.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.
[AI.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 solutions of a quadratic equation results in non-real solutions and write them as a ± bi for real numbers a and b.
[AII.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).