Completing the Square Techniques

The video tutorial introduces the concept of lead coefficients in quadratic equations, starting with a review of a previous problem. It explains how to complete the square when the lead coefficient is one and then extends the method to cases where the lead coefficient is different. The tutorial includes practice problems to reinforce the concepts and concludes with a summary of the key points.

What is a lead coefficient in a polynomial equation?

• The coefficient of the linear term

• The coefficient of the highest degree term

• The sum of all coefficients

• The constant term in the equation

In the equation x^2 + 3x - 5 = 0, what is the lead coefficient?

• -5

• 1

• 5

• 3

What is the first step in completing the square for x^2 + 3x - 5 = 0?

• Multiply by 4

• Rewrite the equation with space for a perfect square

• Divide all terms by 3

• Add 5 to both sides

How do you determine the number to add when completing the square for x^2 + 3x - 5 = 0?

• Add the coefficient of x to the constant term

• Multiply the coefficient of x by 2

• Divide the coefficient of x by 2 and square it

• Square the coefficient of x

What is the result of completing the square for x^2 + 3x - 5 = 0?

• (x + 3)^2 = 29/4

• (x + 3/2)^2 = 29/4

• (x + 3/2)^2 = 9/4

• (x + 3)^2 = 9/4

When completing the square with a lead coefficient other than one, what is the first step?

• Add the lead coefficient to the constant term

• Divide all terms by the lead coefficient

• Multiply all terms by the lead coefficient

• Subtract the lead coefficient from the linear term

In the equation 4x^2 + 3x - 3 = 0, what is the lead coefficient?

• 1

• 3

• -3

• 4

What is the purpose of dividing by the lead coefficient in the equation 4x^2 + 3x - 3 = 0?

• To factor the equation

• To eliminate the constant term

• To make the lead coefficient one

• To simplify the equation

After dividing by the lead coefficient, what is the next step in completing the square?

• Subtract the linear term from both sides

• Multiply all terms by 4

• Rewrite the equation with space for a perfect square

• Add the constant term to both sides

In the equation 5x^2 - x - 2 = 0, what is the lead coefficient?

• 0

• 5

• -1

• 2