Factoring Strategies: Rewriting Expressions

This video tutorial covers various strategies for factoring algebraic expressions. It begins with an introduction to the concept of factoring and proceeds to explain factoring by grouping, including a step-by-step example. The core lesson focuses on factoring expressions completely, emphasizing the importance of identifying and factoring out the greatest common factor. The tutorial also covers the technique of factoring differences of squares and concludes with advanced techniques for more complex expressions. Throughout, the video emphasizes the application of multiple factoring strategies.

What is the first step in factoring by grouping a trinomial?

• Find the square root of the middle term.

• Rewrite the trinomial as a four-term polynomial.

• Factor out the greatest common factor.

• Multiply the first and last terms.

When factoring a difference of two squares, what is the result?

• A trinomial.

• Two conjugate expressions.

• A four-term polynomial.

• A single squared term.

Which of the following is a difference of two squares?

• x^2 - 9x

• x^2 + 9

• x^2 - 4

• x^2 + 4

What is the greatest common factor in the expression 2x^5 + 16x^3 + 30x?

• 30

• 2x

• 16x

• x^2

How can the expression x^4 - 81 be factored completely?

• (x^2 - 9)(x^2 + 9)

• (x - 9)(x + 9)

• (x - 3)(x + 3)(x^2 + 9)

• (x^2 - 81)

What is the first step in factoring the expression 12x^6 - 3x^4 - 54x^2?

• Factor by grouping.

• Complete the square.

• Factor out the greatest common factor.

• Use the quadratic formula.

What is the final factored form of 12x^6 - 3x^4 - 54x^2?

• 3x^2(2x - 3)(2x + 3)(x^2 + 2)

• 3x^2(x^2 - 9)(x^2 + 2)

• 12x^6 - 3x^4 - 54x^2

• 3x^2(x - 3)(x + 3)