Solving Quadratics by Completing the Square

The video tutorial explains the technique of completing the square, a method used to solve polynomials that cannot be factored. It begins with an introduction to the concept and then provides several examples to illustrate the process. The examples demonstrate how to manipulate polynomials into perfect squares, allowing them to be expressed as the square of a binomial, which simplifies solving. The tutorial covers different scenarios, including polynomials with coefficients, and emphasizes the importance of maintaining balance by performing operations on both sides of the equation.

What is the result of factoring the polynomial x^2 + 2x + 1?

• x^2 + 1

• x + 1 times x + 1

• x + 1

• x + 2

When completing the square for x^2 + 2x - 6 = 0, what number is added to both sides to form a perfect square?

• 1

• 2

• 6

• 7

What is the result of taking the square root of both sides in the equation x + 1 = ±√7?

• x = 1 ± √7

• x = ±√7 - 1

• x = ±√7 + 1

• x = 1 - √7

In the equation x^2 + 6x - 2 = 0, what is the value of the term added to both sides to complete the square?

• 3

• 12

• 6

• 9

What is the first step when completing the square for a polynomial with a coefficient on the x-squared term?

• Multiply the coefficient by x

• Divide everything by the coefficient

• Add the coefficient to both sides

• Subtract the coefficient from both sides

What is the least common denominator used when adding fractions 32/12 and 75/12?

• 6

• 36

• 12

• 24

In the equation 3x^2 + 15x - 8 = 0, what is the value of the term added to both sides after dividing by 3?

• 107/12

• 8/3

• 5/2

• 25/4