Navigation

9-12 Integrated Math 3 Unit 2 Lesson 4

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7

Lesson

Lesson 1 Lesson 2 Lesson 3 •Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15

Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 2, Lesson 4

Combining Polynomials

$Course Icon$

Integrated Math 3

Practice

Problem 1

Here are two expressions whose product is a new expression, \(A\).

\(\displaystyle (5x^4 + \boxed{\phantom{33}}x^3)(4x^{\boxed{\phantom{3}}} - 6) = A\)

Andre says that any real number can go in either of the boxes and \(A\) will be a polynomial. Is he correct? Explain your reasoning.

to access Practice Problem Solutions.

Problem 2

Lin divides two polynomials and gets \(0.5x^2 - x + 0.25\). Is this quotient a polynomial? Explain your thinking.

to access Practice Problem Solutions.

Problem 3

What is the result when any 2 integers are multiplied?

a positive integer
a negative integer
an integer
an even number

to access Practice Problem Solutions.

Problem 4

from an earlier course

Write each expression with fewer terms. Show or explain your reasoning.

\((5x) + (x^2 - 4x)\)
\((7x^2 - 2x) + (4x^2 - x)\)
\((x - 8x^2) - (3x^2 + x+ 9)\)
\((2x^3 - x^2) + (5x^2 + 7x^3 - x)\)

to access Practice Problem Solutions.

Problem 5

ForLesson 3: Introducing Polynomials

Identify the degree, leading coefficient, and constant value of each of the following polynomials.

\(f(x)=2x^5 - 8 x^2 - x - 6\)
\(h(x)=x^3 - 7 x^2 - x + 2\)
\(g(x)=5 x^2-4 x^3 + 2x +5.4\)

to access Practice Problem Solutions.

Problem 6

ForLesson 3: Introducing Polynomials

Which point is a relative minimum?

<p>graph with points A, B, C and D plotted. A is a relative minimum. B is on a decreasing portion, C is on a increasing portion, D is a relative maximum</p>

\(A\)
\(B\)
\(C\)
\(D\)

to access Practice Problem Solutions.

Problem 7

from an earlier course

Use the distributive property to rewrite each quadratic expression in standard form. Draw a diagram if needed.

\((x+5)(x-3)\)
\((3x-2)(2x-8)\)

to access Practice Problem Solutions.

Lesson 4 Resources

Student Materials