Combining and Multiplying Polynomials

This video tutorial covers the process of multiplying a binomial by a trinomial, starting with an introduction to the concepts of binomials and trinomials. It provides a detailed example of how to multiply these expressions, highlighting the importance of multiplying each term in the binomial by every term in the trinomial. The tutorial also addresses a common mistake made when cubing a binomial and offers a practice problem to reinforce the learning. The video concludes with a summary and directs viewers to additional resources for further study.

What is a binomial?

• A bracket with four terms

• A bracket with three terms

• A single term

• A bracket with two terms

When multiplying a binomial by a trinomial, what must be done?

• Multiply every term in the binomial by every term in the trinomial

• Multiply only the last terms

• Add the terms together

• Multiply only the first terms

In the example, what is the result of x times 2x?

• 2x

• 4x

• x^2

• 2x^2

What is the common mistake when cubing a binomial?

• Multiplying only once

• Adding the terms

• Not multiplying the entire bracket by itself three times

• Using the wrong formula

What does FOIL stand for in the context of multiplying binomials?

• First, Outer, Inner, Least

• First, Outer, Inner, Last

• First, Only, Inner, Last

• First, Outer, Initial, Last

What is the result of x times x squared in the final example?

• x^2

• x^3

• 2x^2

• 2x^3

What is the final answer after combining like terms in the example?

• x^3 - 6x^2 + 8x - 12

• x^3 - 4x^2 + 12x - 8

• x^3 - 4x^2 + 8x - 6

• x^3 - 6x^2 + 12x - 8

What should you do after multiplying terms in a binomial and trinomial?

• Subtract the terms

• Divide the terms

• Add the coefficients

• Look for like terms and combine them

What is the purpose of the task video mentioned at the end?

• To offer additional practice

• To provide entertainment

• To introduce a new topic

• To summarize the lesson

Where can you learn more about multiplying a binomial by a trinomial?

• In a textbook

• On the website mentioned

• In a different lesson

• In a math competition