# Polynomials

## Objective

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

## Common Core Standards

### Core Standards

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• 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.

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• A.SSE.A.2

## Criteria for Success

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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

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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

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### Problem 1

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

#### Guiding Questions

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### Problem 2

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

#### Guiding Questions

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## Problem Set

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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

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Find all of the roots of the following quartic equation:

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