The lesson covers various factoring techniques, including the greatest common factor, difference of perfect squares, trinomials, and factoring by grouping. It provides exercises to practice these methods and introduces non-standard factoring problems. The lesson emphasizes recognizing structure in expressions to simplify factoring. Advanced techniques for complex problems are also discussed, with a focus on using substitution and identifying patterns.

What is the main focus of this lesson?

• Graphing linear equations

• Using structure to factor

• Solving systems of equations

• Solving quadratic equations

Which type of factoring involves finding a common factor in all terms?

• Factoring by grouping

• Greatest common factor

• Trinomial factoring

• Difference of perfect squares

What is the result of factoring 12x^3 + 20x^2 - 27x - 45 by grouping?

• (4x^2 - 9)(3x - 5)

• (4x^2 + 9)(3x + 5)

• (4x^2 - 9)(3x + 5)

• (4x^2 + 9)(3x - 5)

Which type of factoring is used for the expression 5x + 2 squared minus 2x - 1 squared?

• Greatest common factor

• Difference of perfect squares

• Factoring by grouping

• Trinomial factoring

How can the expression X plus 6 squared plus 2 times X plus 6 minus 35 be simplified?

• (X + 1)(X + 13)

• (X - 1)(X + 13)

• (X + 1)(X - 13)

• (X - 1)(X - 13)

What is the correct factorization of 4x^2 - (x + 5)^2?

• (3x - 5)(x + 5)

• (2x + x + 5)(2x - x - 5)

• (2x - x + 5)(2x + x - 5)

• (3x + 5)(x - 5)

What substitution can simplify the expression 2x + 1 squared minus 2 times 2x + 1 minus 3?

• y = 2x - 1

• y = 2x + 1

• y = x - 1

• y = x + 1

What is the first step in factoring the expression 4x^3(x^2 + 1) - 2x(x^2 + 1)^2?

• Expand the expression

• Combine like terms

• Distribute 4x^3

• Factor out x^2 + 1

How many distinct binomials can the polynomial X^5 + 13X^3 + 36X be factored into?

• Four

• Three

• Six

• Five

What should you always look for first when factoring an expression?

• Difference of perfect squares

• Trinomial structure

• Greatest common factor

• Factoring by grouping