Polynomial Concepts

Unit 3 Polynomials Concepts

19. What is a polynomial?

20. Put a polynomial into standard form, identify the degree and leading coefficient

21. Factor polynomial equations completely using one or more of the following methods: factor out a greatest common factor, use the diamond/box method, split the middle, factor the difference of two squares, use substitution to make a complex problem easier.

22. Determine the multiplicity of factors and how it affects the shape of the graph.

23. Understand how the leading coefficient affects end behavior

24. Understand how the degree determines start/end behavior, the number of turns, the number of roots and the number of x-intercepts.

25. Sketch polynomial graphs from factored form without a calculator.

26. Find a polynomial equation in factored form from its graph including the “a”.


27. Use the quadratic formula to find real and complex roots of polynomials

28. Understand that i =√-1 . Use this to simplify square roots.

29. Use the discriminant to describe the nature of the roots.

30. Use the sum and product of the roots to find a quadratic equation in standard form with integer coefficients

31. Simplify powers of i and perform operations on complex numbers.

32. Solve equations with complex solutions:

28. Use the degree to determine the number of real and complex roots.


29. Polynomial division: grid method, synthetic division

30. Using polynomial division to factor.

31. Finding all roots given only an equation and a graph.

32. Factor the sum and difference of two cubes.

33. Synthetic Division (you can use the box method instead)