Lesson 24

Polynomial Identities (Part 2)

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Is \(a^6 + b^6 = (a^2+b^2)(a^4 - a^2b^2 + b^4)\) an identity? Explain or show your reasoning.

Problem 2

Match each lettered expression with the number of an expression equivalent to it.

Problem 3

Let $(x^2+5x+4)(x+2)=A(x+1)$. If this is an identity, what is a possible expression for $A$?

Problem 4

What are the points of intersection between the graphs of the functions \(f(x)=(x + 6)(2x+1)\) and \(g(x)=2x+1\)?

(From Algebra2, Unit 2, Lesson 11.)

Problem 5

Identify all values of \(x\) that make the equation true.

  1. \(\frac{x+5}{x+11}=\frac{1}{x+5}\)
  2. \(\frac{2x-3}{x} = \frac{14}{x+5}\)
(From Algebra2, Unit 2, Lesson 22.)

Problem 6

Match each expression in the lettered list with the number of an expression equivalent to it.

(From Algebra2, Unit 2, Lesson 23.)