Completing the Square and Binomials

The video tutorial explains how to complete the square for trinomials with a leading coefficient of one. It covers the formula for finding the constant term and demonstrates the process with two examples: one with a positive coefficient and another with a negative coefficient. The tutorial emphasizes the importance of showing work when dealing with fractions and verifies the solutions by factoring the trinomials into binomial squares.

What is the formula for the constant term 'c' in a perfect square trinomial?

• c = b/2

• c = 2b

• c = (b/2)^2

• c = b^2

In the first example, what is the value of 'b' when the coefficient of x is 3?

• 6

• 1.5

• 4.5

• 3

What is the constant term added to form a perfect square trinomial in the first example?

• 3/4

• 9/4

• 3/2

• 6/4

Why is it important to show work when dealing with fractions in completing the square?

• To avoid mistakes

• To make it easier to factor

• To verify the constant term

• All of the above

What are the binomial factors of the trinomial in the first example?

• (x + 3/2)(x + 3/2)

• (x + 3)(x + 3)

• (x + 1.5)(x + 1.5)

• (x + 2)(x + 2)

In the second example, what is the value of 'b' when the coefficient of x is -9?

• -9

• -9/2

• -4.5

• -18

What is the constant term added to form a perfect square trinomial in the second example?

• 81/4

• 36/4

• 18/4

• 9/4

What are the binomial factors of the trinomial in the second example?

• (x - 3)(x - 3)

• (x - 9)(x - 9)

• (x - 4.5)(x - 4.5)

• (x - 9/2)(x - 9/2)

How do you verify that the binomial factors are correct in the second example?

• By checking the sum of the constants

• By checking the difference of the constants

• By checking the product of the constants

• By checking both the product and sum of the constants

What is the final form of the trinomial in the second example?

• (x - 3)^2

• (x - 9/2)^2

• (x - 9)^2

• (x - 4.5)^2