Factoring a quadratic by diamond method

The video tutorial demonstrates how to factor the quadratic expression 64X^2 + 16X + 1. It begins by identifying the expression as a perfect square trinomial, where the product of the coefficients a and c is 64. The tutorial explains that the numbers 8 and 8 multiply to give 64 and add to give 16, confirming the trinomial is a perfect square. The expression is then rewritten as (8X + 1)(8X + 1), and the instructor verifies the factoring by checking each term's multiplication and addition results.

What is the product of the coefficients a and c in the expression 64X^2 + 16X + 1?

• 128

• 64

• 16

• 256

Which two numbers multiply to 64 and add up to 16?

• 12 and 4

• 8 and 8

• 6 and 10

• 4 and 4

Why can't the expression be factored as (X + 8)(X + 8)?

• Because X * X gives 16X^2

• Because X * X does not give 64X^2

• Because 8 * 8 gives 64

• Because 8 * 8 does not give 16

What is the correct factorization of the expression 64X^2 + 16X + 1?

• (8X + 1)(8X + 1)

• (X + 8)(X + 8)

• (16X + 1)(16X + 1)

• (4X + 2)(4X + 2)

What does the term 8X * 1 + 8X * 1 simplify to in the factorization?

• 64X

• 16X

• 32X

• 8X