Solve by factoring when a perfect square

The video tutorial explains how to factor a perfect square trinomial, specifically X^2 + 3/2 X + 9/16. It begins by discussing the challenges of traditional factoring methods and highlights the importance of recognizing perfect squares. The instructor demonstrates the process of factoring by using the properties of perfect squares, verifying the solution, and concluding with the final answer.

What is the main challenge in factoring the expression X^2 + 3/2 X + 9/16?

• Finding two numbers that multiply to 3/2 and add to 9/16

• Finding two numbers that multiply to 3/2 and add to 1/2

• Finding two numbers that multiply to 9/16 and add to 3/2

• Finding two numbers that multiply to 9/16 and add to 1/2

What is the square root of 9/16?

• 3/4

• 1/4

• 1/2

• 3/2

Why is 9/16 considered a perfect square in this context?

• Because 9/16 is a whole number

• Because 9 and 16 are both perfect squares

• Because 9/16 is an integer

• Because 9/16 is a rational number

What is the factored form of the expression X^2 + 3/2 X + 9/16?

• (X - 3/4)(X - 3/4)

• (X + 3/4)(X + 3/4)

• (X - 1/2)(X - 1/2)

• (X + 1/2)(X + 1/2)

What is the solution to the equation (X + 3/4)^2 = 0?

• X = 1/2

• X = -1/2

• X = 3/4

• X = -3/4