Factoring Polynomials: Key Concepts and Techniques

What is the GCF of 24 and 54?

• 18

• 3

• 6

• 12

How does the expression (24y^4 - 54y^3) factor out using GCF?

• 6(4y - 9)

• 6(4y + 9y^3)

• 6(4y^2 - 9y)

• 6(4y - 9y^2)

What is the factored form of a^2 - b^2?

• (a - b)^2

• (a + b)^2

• (a - b)(a + b)

• a^2 + b^2

Using the SOAP method, what does 'S' stand for in the context of factoring cubes?

• Subtract

• Split

• Same

• Square

What is the factored form of x^3 - 343 using the difference of cubes method?

• (x + 7)(x^2 - 7x + 49)

• (x - 7)(x^2 + 7x + 49)

• (x + 7)(x^2 - 7x - 49)

• (x - 7)(x^2 + 7x - 49)

In the x-method for factoring trinomials, what does the top number represent?

• Product of a and c

• Sum of a and b

• Difference of b and c

• Product of b and c

What is the correct next step after applying the x-method and finding the numbers that multiply to the top and add to the bottom?

• Add a, then multiply

• Subtract b, then divide

• Multiply by a, then add

• Divide by a, then slide

What is the factored form of 2h^2 + 5h - 3h - 7.5 using grouping?

• (2h - 3)(h + 2.5)

• (2h + 3.5)(h - 2)

• (2h + 3)(h - 2.5)

• (2h - 3.5)(h + 2)

How is the expression 4q^4 - 13q^2 + 9 factored using the x-method?

• (2q^2 + 1)(2q^2 - 9)

• (2q^2 - 1)(2q^2 + 9)

• (2q^2 + 1)(2q^2 + 9)

• (2q^2 - 1)(2q^2 - 9)

What is the correct factored form of q^4 - 1?

• (q + 1)^2

• (q^2 + 1)^2

• (q + 1)(q - 1)

• (q^2 + 1)(q^2 - 1)