Completing the Square and Trinomials

The video tutorial explains how to complete a perfect square trinomial by adding a constant term to a binomial. It begins by defining a trinomial and a perfect square trinomial, then demonstrates expanding a binomial to understand the pattern. The tutorial shows how to identify the necessary constant by taking half of the linear coefficient, squaring it, and adding it to the expression. Finally, it applies this method to factor the trinomial into a perfect square.

What is a trinomial?

• A polynomial with one term

• A polynomial with four terms

• A polynomial with three terms

• A polynomial with two terms

What is the goal when adding a constant to 2x^2 - 6x?

• To make it a linear equation

• To make it a perfect square trinomial

• To make it a quadratic equation

• To make it a polynomial with four terms

What does (X + a)^2 expand to?

• X^2 + aX + 2a^2

• X^2 + 2aX + 2a^2

• X^2 + aX + a^2

• X^2 + 2aX + a^2

What is the coefficient of the x term in the expression X^2 + 2aX + a^2?

• 2a^2

• a

• 2a

• a^2

How do you determine the constant to add to make a perfect square trinomial?

• Take the square root of the coefficient of x

• Double the coefficient of x

• Take half of the coefficient of x and square it

• Square the coefficient of x

What is half of -6 in the expression 2x^2 - 6x?

• -6

• 6

• -3

• 3

What constant should be added to 2x^2 - 6x to complete the square?

• 12

• 3

• 9

• 6

What is the factored form of x^2 - 6x + 9?

• (X + 3)^2

• (X - 3)(X + 3)

• (X - 3)^2

• (X - 9)^2

What two numbers multiply to 9 and add to -6?

• 3 and 3

• -3 and 3

• -3 and -3

• 9 and -9

What is the final expression after completing the square for 2x^2 - 6x?

• x^2 - 6x + 9

• x^2 - 6x + 6

• x^2 - 6x + 3

• x^2 - 6x + 12