Factoring Cases in Algebra

Which factoring technique would you apply to the expression 6x² + 9x³ - 3x, where a common factor can be extracted?

• Factor out the common factor 3x.

• Factor out the common factor 9x.

• Factor out the common factor 6x.

• Factor out the common factor 2x.

Factor the difference of squares: x² - 49. What are the two binomial factors?

• (x - 1)(x + 1)

• (x - 49)(x + 49)

• (x - 7)(x + 7)

• (x - 14)(x + 14)

Which of the following is the correct factored form of the perfect square trinomial x² + 10x + 25?

• (x + 5)²

• (x + 2)²

• (x - 5)²

• (x + 10)(x + 15)

Factor the sum of cubes: 8x³ + 27. Which expression represents its fully factored form?

• (2x - 3)(4x² - 6x + 9)

• (2x - 3)(4x² + 6x + 9)

• (2x + 3)(4x² + 6x - 9)

• (2x + 3)(4x² - 6x + 9)

When factoring x² - 5x + 6, which pair of numbers satisfies both the product and sum conditions required for trinomial factoring?

• -2 and -3

• -3 and -1

• -4 and -2

• -1 and -6

Factor the difference of cubes: 64x³ - 125. What is the correct factored form using the difference of cubes formula?

• (4x - 10)(16x² + 5x + 25)

• (4x - 5)(16x² + 20x + 25)

• (4x + 5)(16x² - 20x + 25)

• (8x - 5)(8x² + 10x + 25)

Which factoring case applies to the expression 4x² - 12xy + 9y², and what is its fully factored form?

• (4x - 3y)²

• (2x - 3y)²

• (2x + 3y)²

• (2x - 4y)²

Factor by grouping: 3x³ + 6x² + 2x + 4. What are the resulting factors after applying the grouping method?

• (3x² + 1)(x + 4)

• (3x² + 2)(x + 2)

• (3x² + 4)(x + 1)

• (6x² + 2)(x + 2)

Which of the following expressions is a prime polynomial that cannot be factored further over the integers: x² + 9, x² - 9, x² - 6x + 9, or x² + 6x - 9?

• x² - 9

• x² + 9

• x² + 6x + 9

• x² - 6x - 9

Factor completely: 2x⁴ - 32. Which combination of factoring cases (GCF, difference of squares) must be applied to reach the fully factored form?

• Difference of squares only

• GCF and trinomial factoring

• Sum of cubes and GCF

• GCF and difference of squares