Polynomials

Lesson 11

Objective

Factor polynomials by grouping in quartic, cubic, and quadratic functions.

Common Core Standards

Core Standards

?

  • F.IF.C.8.A — Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Foundational Standards

?

  • A.SSE.A.2

Criteria for Success

?

  1. Identify the greatest common factor and difference of squares within four-term functions, and re-arrange terms to highlight these patterns.
  2. Group and factor terms to identify the linear factors embedded.
  3. Determine when a combination of strategies must be used to factor a polynomial, including the quadratic formula.
  4. Utilize efficient methods to finding the solution to polynomial functions.

Tips for Teachers

?

We will not be using the rational roots theorem, so ensure that the problems you provide are factorable using one of the methods determined in this unit so far.

Anchor Problems

?

Problem 1

Find the roots of the function $${f(x)=9x^3+36x^2-4x-16}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Find the roots of the function $${g(x)=x^4-x^2-12}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

?

The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include a variety of factoring problems that utilize degrees from 2 to 4 and patterns that require use of difference of squares, difference and sum of cubes, and factoring by grouping.

Target Task

?

Find all of the roots of the following quartic equation: 

$${h(x)=x^4-2x^3-9x^2-18x}$$