Factoring and Polynomial Operations

This video tutorial covers algebra topics from the Algebra 1 Keystone review packet, focusing on problems 17 through 22. It begins with adding and subtracting polynomials, emphasizing the importance of combining like terms and distributing negative signs. The tutorial then moves on to multiplying binomials and trinomials, demonstrating the distribution of terms. Finally, it covers factoring polynomials, including recognizing the difference of squares and factoring completely. The video provides step-by-step instructions and strategies for solving these algebraic problems.

When adding polynomials, what is the key step to ensure terms are combined correctly?

• Ignoring the variables

• Distributing the coefficients

• Multiplying the terms

• Aligning like terms

In polynomial subtraction, what is crucial to remember about the minus sign?

• It should be added to the coefficients

• It only affects the first term

• It should be distributed across the polynomial

• It can be ignored

What is the first step in multiplying a binomial by a trinomial?

• Factor the trinomial

• Combine like terms

• Distribute the first term of the binomial

• Add the coefficients

How do you handle like terms when multiplying polynomials?

• Ignore them

• Align them for addition

• Subtract them

• Multiply them separately

What is a difference of squares in factoring?

• A subtraction of two perfect squares

• A division of two terms

• A sum of two squares

• A product of two identical terms

When factoring x^4 - 1, what is the first step?

• Combine like terms

• Recognize it as a difference of squares

• Add a middle term

• Multiply the terms

What is the first step in factoring a perfect square trinomial?

• Look for a GCF

• Identify the square of a binomial

• Multiply the terms

• Add the coefficients

How do you recognize a perfect square trinomial?

• It is a sum of two squares

• It has no middle term

• It is a product of two identical terms

• It has a middle term that is twice the product of the square roots of the first and last terms

What is the key to factoring a general trinomial?

• Dividing the middle term by the last term

• Subtracting the first term from the last

• Adding all terms together

• Finding two numbers that multiply to the last term and add to the middle term

In the expression x^2 - 3x - 18, which pair of numbers is used for factoring?

• 8 and 1

• 5 and 5

• 6 and 3

• 9 and 2