Factoring Polynomials and Expressions

The video tutorial covers the process of factoring quadratic expressions with different variables. It begins with factoring 3a² - 24ab + 48b² by identifying common factors and using the quadratic formula. The next section focuses on factoring x² - 11x + 24, explaining how to find two numbers that add to -11 and multiply to 24. The tutorial then addresses factoring 9t² + 12t + 4, demonstrating the use of binomials. Finally, it explains the complete factorization of 32 - 8z², highlighting the difference of squares method.

What is the first step in factoring the expression 3a^2 - 24ab + 48b^2?

• Add a constant to both sides

• Identify two numbers that multiply to 48

• Rewrite the expression in terms of x

• Factor out the greatest common factor

Which of the following is the factored form of 3a^2 - 24ab + 48b^2?

• 3(a + 8b)(a - 6b)

• 3(a - 4b)^2

• 3(a + 4b)^2

• 3(a - 8b)(a + 6b)

How do you determine the two numbers needed to factor x^2 - 11x + 24?

• Find two numbers that add to -24 and multiply to 11

• Find two numbers that add to 11 and multiply to 24

• Find two numbers that add to -11 and multiply to 24

• Find two numbers that add to 24 and multiply to -11

What is the factored form of x^2 - 11x + 24?

• (x - 8)(x + 3)

• (x + 8)(x - 3)

• (x - 8)(x - 3)

• (x + 8)(x + 3)

What is the first step in factoring 9t^2 + 12t + 4?

• Identify the square root of the first term

• Use the quadratic formula

• Factor out the greatest common factor

• Complete the square

Which expression represents the complete factorization of 9t^2 + 12t + 4?

• (3t - 4)(3t + 1)

• (3t + 2)^2

• (3t - 2)^2

• (3t + 4)(3t - 1)

What is the first step in factoring 32 - 8z^2?

• Complete the square

• Use the quadratic formula

• Factor out the greatest common factor

• Identify the square root of the first term

Which of the following is the factored form of 32 - 8z^2?

• 8(z + 2)(z - 2)

• -8(z + 2)(z - 2)

• 8(z - 2)(z + 2)

• -8(z - 2)(z + 2)

What pattern is used to factor the expression 32 - 8z^2?

• Difference of cubes

• Perfect square trinomial

• Difference of squares

• Sum of squares

What is the result of factoring 32 - 8z^2 using the difference of squares?

• 8(z + 2)(z - 2)

• 8(z + 4)(z - 4)

• -8(z + 2)(z - 2)

• -8(z + 4)(z - 4)